   Chapter 11.FOM, Problem 6P ### 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

# Here is a data matrix for a line drawing: D = [ 0 1 2 1 0 0 0 0 2 4 4 0 ] (a) Draw the image represented by D .(b) Let T = [ 1 1 0 − 1 ] . Calculate the matrix product T D , and draw the image represented by this product. What is the effect of the transformation T ?(c) Express T as a product of a shear matrix and a reflection matrix. (See Problem 2.) 2 . 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

(a)

To sketch:

The image represented by D matrix.

Explanation

Given:

The data matrix is

D=

Approach:

Plot the points on the graph and join them by a line segment

To determine

(b)

To find:

The matrix product TD and the effect of transformation T.

To determine

(c)

To show:

T is a product of shear matrix and a reflection matrix.

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