   Chapter 11.FOM, Problem 2P ### 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

# Verify that multiplication by the given matrix has the indicated effect when applied to the gray square in the table. Use c = 3 in the expansion matrix and c = 1 in the shear matrix. T 1 = [ − 1 0 0 1 ] Reflection in y − axis T 2 = [ 1 0 0 c ] Expansion (or contraction) in y − direction T 3 = [ 1 0 c 1 ] Shear in y − direction

To determine

To verify:

The three transformations of the gray square have indicated effect.

Explanation

Given:

The vertices of the gray square are:

, , , and .

c=3 in expansion matrix and c=1 in the shear matrix.

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 yaxis

T=

Expansion in ydirection

T=[100c]

Shear in ydirection

T=[10c1]

Calculation:

The data matrix is given by

D=

Plot the points on the graph and connect them by a line segment.

Figure 1

Multiply the D matrix by appropriate transformation matrix.

(1) Reflection in yaxis: Apply reflection transformation

T=

The following matrix is obtained

TD==

Obtain the resulting graph by plotting the points and joining them by a line

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