4. Find the coordinates of the vertices of the rectangleWXYZ with coordinates W(0, – 7), X(2, 2), Y(−11, — 12), Z(–5, 10)after a dilation with a scale factor of 2. Write the answeras a matrix.-9-31-5 4 -10 12O 20 4 -22 -10]-14 4 -24 20[-14O 2 -11 -51°[º-7 2 -12 10[20 13 79 0 14

Here we use the properties of transformation rules of function. In the dilation of a triangle we…

Answered: 4. Find the coordinates of the vertices…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.1: Matrix Operations

Problem 39EQ

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Show that the three points (x1,y1)(x2,y2) and (x3,y3) in the a plane are collinear if and only if the matrix [x1y11x2y21x3y31] has rank less than 3.
Consider the matrices R=[ 0110 ] H=[ 1001 ] V=[ 1001 ] D=[ 0110 ] T=[ 0110 ] in GL(2,), and let G={ I2,R,R2,R3,H,D,V,T }. Given that G is a group of order 8 with respect to multiplication, write out a multiplication table for G. Sec. 3.3,22b,32b Find the center Z(G) for each of the following groups G. b. G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of section 3.1. Find the centralizer for each element a in each of the following groups. b. G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of section 3.1 Sec. 4.1,22 22. Find an isomorphism from the octic group D4 in Example 12 of this section to the group G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of Section 3.1. Sec. 4.6,14 14. Let G={ I2,R,R2,R3,H,D,V,T } be the multiplicative group of matrices in Exercise 36 of section 3.1, let G={ 1,1 } under multiplication, and define :GG by ([ abcd ])=adbc. Assume that is an epimorphism, and find the elements of K= ker . Write out the distinct elements of G/K. Let :G/KG be the isomorphism described in the proof of Theorem 4.27, and write out the values of .
a Let T=[3001]. What effect does T have on the gray square in Table 1? b Let S=[1002]. 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=TS. e Apply the transformation W to the square. Compare to you final result in part c. What do you notice?
Find conditions on w,x,y,andz such that AB=BA for the matrices below. A=wxyz and B=11-11
Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. Determine whether the columns of matrix A span R4. A=[1210130200111001]

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4. Find the coordinates of the vertices of the rectangle WXYZ with coordinates W(0, - 7), X(2, 2), Y(−11, − 12), Z(−5, 10) after a dilation with a scale factor of 2. Write the answer as a matrix. 2 4 -9 -3] 4 -10 12 °[ 4 -22 -10 -14 4 -24 20 O °[ O 2 -11 -57 47 -7 2 -12 10 [20 13 7 9 0 14