QUESTION 3 Let B = {(1, 5), (-5, -24)} and B' = {(-28, -134), (-36, -171)} be bases for R2, and let 4 4 2 be the matrix for T: R" + R' relative to B. Use the transition matrix I from B' to B and matrix A to find [ VJ; and [7(v)]s where [v]s' You may use MATLAB for matrix operations. The transition matrix P from B' to B is QUESTION 4 Use the transformation defined by T(v1,v2,v3) = (2v1+v2, v1-v2) to find the image of v = (1, 2, 5) O (5, -1) O (-1, 4) O (4, -1) O (4, -1, 0) O (5, 1)QUESTION 5 Find the standard matrices for the composite transformations T = T 2 T 1 and T' =T 1 T 2 , where 1: RR , Ti(x, y)= (x - 3y, 3x +6y) and T2: R-R2 , T,(x, y) = (3x, 7x -5y). O None of the answers QUESTION 6 Given the transformation T: RS -> RS defined by the rule T(x, y, z) = (-3x, - 7y, 5z) in the standard basis for RS and a basis B' = {(1, 1, 0), (1, 0, 1), (0, 1, 1)}. Let [VIB' = (1, 1, -1) , Which of the following statements are true? (Check all that apply). MATLAB may be used for matrix operations. - 4 The matrix representation for T in basis B' is AB' = 2 4 The coordinates of the image of vector v in the standard basis [T(V)Is = (-6, 0, 0) The coordinates of the image of vector v in the standard basis [T(v)Is = (-3, 0, 0) T The coordinates of vector v in the standard basis [vIs = (2, 0, 0) The coordinates of the image of vector v in basis B', [T(V)]B' = (-3, -3, 3) TQUESTION 7 Use the transformation defined by T(V 1, v 2) = (4v 1 - 6v 2, 5v 1 + 2v 2 , v 2) to find the image of the vector v = (1, -1). O (10, -3, -1) O (10, 3, 1) O (3, -1, 10) O (10, -3, 1) O (10, 3, -1) QUESTION 8 Given a transformation T: RS - R defined as T(x, y, z) = (x+y+Z, -x+2z, 2y-z) in the standard basis. Let B = {(2, 0, 1), (0, 2, 1), (1, 2,1)}, B' = {(1, 1, 1), (1, 1, 0), (0, 1,1)} two bases in RS and v = (4, -5, 10) in the standard basis. Which of the following statements are true? (Check all that apply) MATLAB may be used for matrix operations. T(v) in the standard basis is (9, 16, -20) T(v) in basis B' is (-27, 36, 7) 2 4 6 The matrix App: relative to B and B' defined as [7(V)]B' = ABB' [v]B is 1 -1 - 2 -1 -3 T(v) in basis B is (25/2, 37/2, -21) O T(v) in basis B is (-28, -57, 65) TQUESTION 9 Let T: V-> W be the transformation represented by T(x) = Ax, Which of the following statements are true? (Check all that apply) -2 1 07 A= 1 23 10 0 0 1] IT is onto O dim V = 4 and dim W = 3 O rank(T) = dim V O The basis for range (T) has three vectors O T is not onto QUESTION 10 Use the transformation defined by T(V 1: v 2) = (4v 1 - 6v 2, 5v 1 + 2v 2. v 2 ) to find the preimage of (10, 3, -1) O (t, -2t), where t is any real number O (1, -1) O (1, -t), where t is any real number O (2, -1) O (1, -1, t), where t is any real number