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Q26E

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Linear Algebra With Applications
Found in: Page 54
Linear Algebra With Applications

Linear Algebra With Applications

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(x)=Ax on this face.

26. [0110]

By an angle of 90 , the face gets rotated clockwise.

See the step by step solution

Step by Step Solution

Step by Step Explanation: Step 1: Consider the matrix

Let the matrix be,

A=0110

Then,

Tx=AxTx=0110x

Step 2: Compute the matrix

The matrix is,

T(x)=[0110]x1x2T(x)=[x2x1]

Step 3: Graph the matrix

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

Hence, T(x) is obtained by rotating the vector x through an angle of 90° in the clockwise direction.

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