QUESTION 3.1 Computing linear transformation matrix from non-standard basis Choose one . 5 points Find the matrix of T relative to the basis By = (01, U2) = {(2, 1), (3, 2)} and Be = {w1, w2} = {(1, 1), (1, 2)} That is : [TIB_,B. = [Mc | Mu] O [TIB.B. = 3 6) O 11/3 -2 O QUESTION 3.2 Computing a vector image using transition matrix Choose one . 5 points Using previous question 3.1 answer for [Tlg_,B.- calculate [ula, if [ula = ( ) using O B. = (3 ) O -28/3 O Lu = 2QUESTION 14 Inverse Scaling Matrix Choose one . 5 points What is the inverse matrix of the scaling matrix with scaling factors SI = 4 , Sy = 2 and $1 = 1 O 1 0 1/4 0 1 1/2 0 1 O 0 S= 1/2 0 1/4 O 1/4 0 0 S = 1/2 0 0 QUESTION 15 V Linear Operators Choose all that apply . 5 points Which of the following linear transformations are linear operators ? T : R3 + 1R3 such that T(1, y) = (1 - 2y, y) OT : R2 + IR such that T(1, y) = 1 - 2y T: R3 + 1RX3 such that T(z, y) = (1 - y,y, I + y) T: 13 + R' such that T(z, y, 2 ) = (1 - 2y - z, y, I t y + z)QUESTION 11 V image of a point by rotation Choose one . 5 points What is the image of p = (1, -1, 0) after a rotation of 90 about the z-axis? O = O = OQUESTION 10 V Inverse of a Rotation Matrix Choose one . 5 points Write the inverse rotation matrix about the z-axis with angle 90 where cos(90) =0 and sin (90) = 1 O -1 0 0 0 0 0 O 0 -1 R, ' (1/2) = 0 0 O 0 1 0 R, ' (1/2) = -1 0 0 0 0 1Inverse Translation matrix Choose one . 5 points What is the inverse matrix of the translation in the direction of u = (1, 2, 3) from the previous question 6? - 2 O T-1= 1/2 1/3 0 O 0 1 01 -3 0 0 0 1 QUESTION 9 Rotation Matrix in 3D Space. Choose one . 5 points Write the rotation matrix about the z-axis with angle 90 where cos(90) =0 and sin(90) = 1. note that: 90(degree) = x/2(radian) O -1 0 R=(1/2) = 0 0 O -1 0 R=(1/2) = 0 0 0 1 O 1 0 R=(1/2) = 0 0 0 0 0 1QUESTION V Image of a point by translation Choose one . 5 points What is the image of p = (4, 5, 2) after the translation in the direction of 3 = (1, 2, 3) from the previous question 6? O O 10 Or P = 10 6 O Or PQUESTION 6 Translation in 3D Space Choose one . 5 points Write the translation matrix in the direction of v = (1, 2,3) O 0 1 0 1 3 0 0 2 O 1 0 0 0 0 Toll,2,3) = 0 0 30 0 0 0 1 O 1 0 1 \\ 0 102 Tol,2,3) = 0 1 3 0 0 1