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Exercises and solutions
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‎Linear_Transformations_Solutions.ipynb‎

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},
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{
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"cell_type": "markdown",
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"id": "015b5f1e",
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"id": "62aee880",
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"metadata": {},
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"source": [
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"**Exercise 1:** \n",
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"\n",
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"($a$) Find a matrix that represents the reflection about the $x_1$-axis. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "78651a33",
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here."
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]
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},
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{
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"cell_type": "markdown",
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"id": "06d562bd",
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"metadata": {},
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"source": [
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"($b$) Multiply the matrix by $\\texttt{coords}$ and plot the results."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "b247b340",
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here."
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]
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},
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{
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"cell_type": "markdown",
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"id": "070a66f3",
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"metadata": {},
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"source": [
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"**Exercise 2:** \n",
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"\n",
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"($a$) Find a matrix that represents the reflection about the line $x_1=x_2$. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "daabb7a4",
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here."
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]
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},
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{
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"cell_type": "markdown",
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"id": "19951e66",
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"metadata": {},
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"source": [
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"($b$) Multiply the matrix by $\\texttt{coords}$ and plot the results."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "172d37ad",
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here."
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]
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},
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{
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"cell_type": "markdown",
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"id": "50c673a0",
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"metadata": {},
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"source": [
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"**Exercise 3:** \n",
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"\n",
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"($a$) Find a matrix that represents the rotation clockwise by an angle $\\theta$. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "8ba3c450",
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here."
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]
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},
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{
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"cell_type": "markdown",
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"id": "5ed5fb51",
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"metadata": {},
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"source": [
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"($b$) Let $\\theta = 90^{\\circ}$. Multiply the matrix by $\\texttt{coords}$ and plot the results."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "67c3e025",
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here."
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]
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},
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{
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"cell_type": "markdown",
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"id": "015b5f1e",
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"metadata": {},
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"source": [
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"**Exercise 4:** \n",
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"\n",
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"$(a)$ Find a matrix that represents a vertical shear followed by the rotation in Example 3. "
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]
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},
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},
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{
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"cell_type": "markdown",
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"id": "ffc4c0b9",
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"id": "2de820c9",
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"metadata": {},
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"source": [
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"**Exercise 2:** \n",
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"\n",
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"Create a new matrix of coordinates, apply one of the transformations in the Examples and plot the results."
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"**Exercise 5:** Create a new matrix of coordinates and apply one of the transformations in the Examples. Plot the results."
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]
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},
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{
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"ax.set_aspect('equal')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "81b72e12",
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"metadata": {},
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"source": [
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"**Exercise 6:** \n",
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"\n",
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"($a$) Construct a matrix that represents a horizontal and a vertical stretch by a factor of 2 . "
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "41c66dad",
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here"
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]
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},
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{
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"cell_type": "markdown",
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"id": "f9d40e46",
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"metadata": {},
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"source": [
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"($b$) Create a new matrix of coordinates. Apply this transformation and plot the results."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "2f048b8d",
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here"
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]
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},
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{
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"cell_type": "markdown",
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"id": "374361cf",

‎Planar_Transformations.ipynb‎

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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Exercises\n",
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"\n",
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"### Exercises"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Exercise 1:** \n",
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"\n",
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"($a$) Find a matrix that represents the reflection about the $x_1$-axis. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"($b$) Multiply the matrix by $\\texttt{coords}$ and plot the results."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Exercise 2:** \n",
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"\n",
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"($a$) Find a matrix that represents the reflection about the line $x_1=x_2$. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"($b$) Multiply the matrix by $\\texttt{coords}$ and plot the results."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Exercise 3:** \n",
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"\n",
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"($a$) Find a matrix that represents the rotation clockwise by an angle $\\theta$. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"($b$) Let $\\theta = 90^{\\circ}$. Multiply the matrix by $\\texttt{coords}$ and plot the results."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Exercise 4:** \n",
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"\n",
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"($a$) Find a matrix that represents a vertical shear followed by the rotation in Example 3. "
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]
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},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Exercise 2:** Create a new matrix of coordinates, apply one of the transformations in the Examples and plot the results."
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"**Exercise 5:** Create a new matrix of coordinates and apply one of the transformations in the Examples. Plot the results."
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]
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},
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{
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"source": [
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"## Code solution here."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Exercise 6:** \n",
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"\n",
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"($a$) Construct a matrix that represents a horizontal and a vertical stretch by a factor of 2 . "
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"($b$) Create a new matrix of coordinates. Apply this transformation and plot the results."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"## Code solution here"
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]
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}
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],
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"metadata": {

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