Please Write Neatly So I Can Understand

Question 1

Let B = {(1, 2), (1, 1)} and 3' = {(4, 1), (o, 2)} be bases for R2, and let 0 -1 A ' 2 1 be the matrix for T: R2 > R2 relative to B. (a) Find the transition matrix P from B' to B. . u. II (b) Use the matrices P and A to find [V]B and [T(v)]5 , where [V13'= [1 2]T. ? |_| U3 II 2 n It [T(V)]B 1 1: II (c) Find P'1 and A' (the matrix for T relative to B'). .- -1: P -o ll \fLet B = {(1, 0, 1), (0, 1, 1), (1, 1, 0)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R3, and let 1 5 2'1 2 _ _; 1 A' 2 2 2 1 1 2 1 2 be the matrix for T: R3 > R3 relative to B. (a) Find the transition matrix P from B' to B. 112 -1l2 1l2 .- P = -112 112 1l2 _. 112 112 -11'2 l I V (b) Use the matrices P and A to find [V]B and [T(v)]5, where [V]3'= [1 -1 0]T- ii \f\fSuppose A is the matrix for T: R3 > R3 reiative to the standard basis. Find the diagonal matrix A' for T relative to the basis 8'. 020 A=110, 00-1 3' = {(-1, 1, 0). (2. 1, 0), (0. 0. 1)} .2 o o - A,= o 1 o _. o o .2 l t Suppose A is the matrix for T: R3 . R3 relative to the standard basis. Find the diagonal matrix A'for T relative to the basis 5'. i _i 2 '1 2 _ 1 i A 2 2 2 , 3 1 2 1 2 B, = {(11 1: _1)l (1: _1I 1)I(_1I 1: 1)} A! ll ll \f