   Chapter 11.FOM, Problem 4P ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# (a) Let T = [ 3 0 0 1 ] . What effect does T have on the gray square in Table 1?(b) Let S = [ 1 0 0 2 ] . What effect does S have on the gray square in Table 1?(c) Apply S to the vertices of the square, and then apply T to the result. What is the effect of the combined transformation?(d) Find the product matrix W = T S .(e) Apply the transformation W to the square. Compare to you final result in part (c). What do you notice?

To determine

(a)

To find:

The effect of T on the gray square.

Explanation

Given:

The vertices of the gray square are:

, , , and .

T=

Approach:

Multiplication of Matrices:

If A is a m×n matrix and B is a n×p matrix, then the product AB is the m×p matrix whose ijelement is the inner product of the ith row of A and jth column of B.

Transformation matrix:

Reflection in xaxis

T=

Expansion in xdirection

T=[c001]

Shear in xdirection

T=[1c01]

Gray square in Table 1

To determine

(b)

To find:

The effect of S on the gray square.

To determine

(c)

To find:

The effect of combined transformation of S and T on the gray square.

To determine

(d)

To find:

The product matrix W=TS.

To determine

(e)

To compare:

The transformation W applied to the square with the result in part (c).

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