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Chapter 2: Q27E (page 54)

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)鈫�=Ax鈫�on this face.

27.[100-1]

Short Answer

Expert verified

By an angle of 180鈭�, the face gets rotated clockwise, that is, reflection about y-axis.

The required graph is,

Step by step solution

01

Step by Step Explanation: Step 1: Consider the matrix

Let the matrix be,

A100-1

Then,

T(x)鈫�=Ax鈫�T(x)鈫�=[100-1]x鈫�

02

Compute the matrix

The matrix is,

T(x)鈫�=[100-1][x1x2]鈭�T(x)鈫�=[x1-x2]

03

Graph the matrix

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

Hence, T(x)鈫�is obtained by rotating the vector x鈫� through an angle of 180鈭�in the clockwise direction, that is, reflection about y-axis.

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Most popular questions from this chapter

TRUE OR FALSE?

The formula rref(AB) =rref(A)rref(B)holds for alln脳p matrices A and for allp脳m matrices.

Write all possible forms of elementary2脳2E5=10k1matrices E. In each case, describe the transformationy鈫�=Ex鈫�geometrically.

There exists a regular transition matrix A of size 3 脳 3 such that A2=A.

Question: Show that if A and B are nxn transition matrices, then AB will be a transition matrix as well. Hint: Use Exercise 67b.

TRUE OR FALSE?

A=[11/201/2] is a regular transition matrix.
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