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Q28E

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Found in: Page 54

### Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

# Consider the circular face in the accompanying figure. For each of the matrices A in Exercises 24 through 30, draw a sketch showing the effect of the linear transformation${\mathbit{T}}\stackrel{\mathbf{\to }}{\left(x\right)}{\mathbf{=}}{\mathbit{A}}\stackrel{\mathbf{\to }}{\mathbf{x}}$on this face.28. $\left[\begin{array}{cc}1& 0\\ 0& 2\end{array}\right]$

By a factor of$2$, the face gets scaled along y-axis.

The required graph is,

See the step by step solution

## Step by Step Explanation: Step 1: Consider the matrix

Let the matrix be,

$A=\left[\begin{array}{cc}1& 0\\ 0& 2\end{array}\right]$

Then,

localid="1659703886095" $T\stackrel{\to }{\left(\mathrm{x}\right)}=A\stackrel{\to }{\mathrm{x}}\phantom{\rule{0ex}{0ex}}T\stackrel{\to }{\left(\mathrm{x}\right)}=\left[\begin{array}{cc}1& 0\\ 0& 2\end{array}\right]\stackrel{\to }{\mathrm{x}}$

## Step 2: Compute the matrix

The matrix is,

$T\stackrel{\to }{\left(\mathrm{x}\right)}=\left[\begin{array}{cc}1& 0\\ 0& 2\end{array}\right]\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\end{array}\right]\phantom{\rule{0ex}{0ex}}T\stackrel{\to }{\left(\mathrm{x}\right)}=\left[\begin{array}{c}{x}_{1}\\ 2{x}_{2}\end{array}\right]$

## Step 3: Graph the matrix

Now, graph the obtained vectors on the given circular face.

Hence, $T\stackrel{\to }{\left(\mathrm{x}\right)}$ is obtained by scaling the vector$\stackrel{\to }{\mathrm{x}}$ by a factor of $2$ .