For each of the following pairs of ordered bases B and ß' for R2, find the change of coordinate matrix that changes B'-coordinates into B- coordinates. (a) B = {e1,e2} and ß' = {(a1, a2), (b1, b2)} b) ß = {(-1,3), (2, –1)} and ß' = {(0, 10), (5,0)} (c) ß = {(2,5), (-1, –3)} and ß' = {e1,e2} d) B = {(-4,3), (2, –1)} and ß' = {(2, 1), (-4, 1)} %3D %3D %3D %3D %3D %3D %3D

Find the determinant of the matrix. [4032013501511103]

Let B = {(1,3), (-2,-2)} and B' = {(-12,0), (-4,4)} be bases for R2, and let  A= 4 3 0 2 be the matrix for T: R2 -> R2 relative to B

1 -2 -{[3][7]} and C={[G7] [7]} 4 9 3. Let B = a. Find the change of coordinate matrix from C to B.

Identify the matrix that represents each linear transformation below. Write A, B, C, D, D or F. 20 -2 0 A = B= = 02 0 -√212 √212 (39), ^ - (² :) " - ( - ² - 2).C-( √²/2 √212) P-(-03). E-(0-²). 2 D= E= 20 and F= √212-√212 √212 √212 1. Clockwise rotation by an angle of 450 is associated to matrix 2. Counterclockwise rotation by an angle of 45° is associated to matrix 3. Clockwise rotation by an angle of 90° is associated to matrix 4. Counterclockwise rotation by an angle of 900 is associated to matrix 5. A dilation by a factor of 2 is associated to matrix 6. Reflexion about the origin and a dilation by a factor of 2 is associated to matrix Hint: Draw a vector and its image under each transformation.

Section 2.5: Number 2(b, d)only!