Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

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 $T \vec{(x)} = A \vec{x}$ on this face.
28. $[\begin{matrix} 1 & 0 \\ 0 & 2 \end{matrix}]$

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

The required graph is,

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step by Step Explanation: Step 1: Consider the matrix

Let the matrix be,

$A = [\begin{matrix} 1 & 0 \\ 0 & 2 \end{matrix}]$

Then,

localid="1659703886095" $T \vec{(x)} = A \vec{x} T \vec{(x)} = [\begin{matrix} 1 & 0 \\ 0 & 2 \end{matrix}] \vec{x}$

Step 2: Compute the matrix

The matrix is,

$T \vec{(x)} = [\begin{matrix} 1 & 0 \\ 0 & 2 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \end{matrix}] T \vec{(x)} = [\begin{matrix} x_{1} \\ 2 x_{2} \end{matrix}]$

Step 3: Graph the matrix

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

Hence, $T \vec{(x)}$ is obtained by scaling the vector $\vec{x}$ by a factor of $2$ .

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Linear Algebra With Applications

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Short Answer

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 $T \vec{(x)} = A \vec{x}$ on this face.
28. $[\begin{matrix} 1 & 0 \\ 0 & 2 \end{matrix}]$

Step by Step Solution

Step by Step Explanation: Step 1: Consider the matrix

Step 2: Compute the matrix

Step 3: Graph the matrix

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Linear Algebra With Applications

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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 transformationT(x)→=Ax→on this face.28. [1002]

Step by Step Solution

Step by Step Explanation: Step 1: Consider the matrix

Step 2: Compute the matrix

Step 3: Graph the matrix

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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 $T \vec{(x)} = A \vec{x}$ on this face.
28. $[\begin{matrix} 1 & 0 \\ 0 & 2 \end{matrix}]$