Let B = {(0, 1, 1), (1, 0, 1), (1, 1, 0)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R3, and let -1 5 A 1 2 be the matrix for T: R3 → R3 relative to B. (a) Find the transition matrix P from B' to B. P = (b) Use the matrices P and A to find [V]g and [7(V)]g, where [V]g = [1 -1 0j". [V]B [T(V)]B = m/N -/2 1/2

Let B={(1, 0), (0, 1)} and B'= {(1, 2), (2, 3)} be any two bases of R². Then verify PT],P= [T], where T(x, y)=(2x-3y, x +y) and P is the B'> transition matrix from B to B'.

Let B = {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)) be bases for R³, and let 1 2 1 2 A = P = 22555T 4 be the matrix for T: R3 R3 relative to B. [V] B -1 a) Find the transition matrix P from B' to B. 2 = 1 (b) Use the matrices P and A to find [v] and [T(v)]B, where [v] [-1 1 0]. [T(V)]B = 1

Consider the ordered bases B = ((-5, 3), (-2, 1)) and C = ((2, 1), (-3,4)) for the vector space R². a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, 1)). TE b. Find the transition matrix from B to E. TE c. Find the transition matrix from E to B. d. Find the transition matrix from C to B. TB == 10 e. Find the coordinates of u [U]B=TB[U]E. [u]B == (-2, 2) in the ordered basis B. Note that f. Find the coordinates of v in the ordered basis B if the coordinate vector of vin C is [v] c = (1,2). [V]B=

Let 8 = {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and 8¹ = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R², and let be the matrix for 7: R³ R³ relative to 8. (a) Find the transition matrix P from B' to 8. U 1 -1 -888 0 x (b) Use the matrices P and A to find [v]g and [7(v)]g, where [v], [-1 1 0] ↓↑ [7(v)] = 8 ↓↑ (c) Find A and A' (the matrix for 7 relative to 8). p-1= A'= (d) Find [7(v)]g two ways. [7(v)] = P¹[7(v)] = [7(v)] = A'[v] = [v] = 000-000-

1. Let u₁, U2, U3 } and { V₁, V2, V3 } be ordered bases for R³, where H and U₁ = 2 1 U₂ = 1 V1 = 1 -1 -2 U3 = -8-0-0 V2 = 1 V3 (a) Determine the transition matrix corresponding to a change of basis from the ordered basis {u₁, U2,, u3} to the ordered basis {V₁, V2, V3}. (b) Write vector z = 2u₁ - 3u₂ + u3 as Use this transition matrix to find the coordinates of with respect to {V₁, V2, V3}.

5) PLEASE ANSWER EACH QUESTION, THANKS.

Find the transition matrix from the basis B = {(1,2,3) (1,0,1)(1,2,1)} to B' = {(1,1,0)(0,1,1)(1,1,1)}.