Let B = {(1, 3), (-2,-2)) and B' = {(-12, 0), (-4, 4)) be bases for R2, and let A = 02 be the matrix for T: R2 R2 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)]B, where [v]= [-14]. [v]8 = [T(V)]8 = (c) Find P¹ and A' (the matrix for 7 relative to B'). p-1 = QED 1 A¹ = 1

Q: Let C be an nxn matrix that satisfies C2 -3C–2In 0. Show that C is invertible and C=1 = }(31-A)

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Q: ) If the matrix A= [4 2 1; 1 5 9; 3 8 7], find: · A' - A(3,1) - size(A) - A(:,2)= [] Inv(A)

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Q: 1. Let B = {(1,3), (–2, –2)} and B' = {(-12,0), (-4, 4)} be bases for R2, and let A = be the matrix…

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Q: a) For invertible matrices A, BE R™×", show that ((AB)")-1 = (A-1)" (B1)". b) Let A, B, C, D e R"*"…

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Q: Given bases 2 -2 C = { for R. 2 -2 1 find chang-of-coordinates matrices Pc¬B and PB-»c•

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Q: If the matrix of change of basis form the basis B to the basis B'is A= OA °;) 0⁰ (²) -3 2 then the…

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Q: 2)} and 0 4 A = 2 3 . be the matrix for T: R2 → R? relative to (a) Find the transition matrix P

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Q: Let J„ be the n × n matrix whose entries are all equal to 1, and let D(^1, ... , An) be the n × n…

A: The complete solutions are given below

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Q: Given A = and B %3D Find the matrix represented by: (iii) 3(2B – 4A) (iv) A + 3AT

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Q: If the matrix A= [2 5 1;7 3 6;2 5 4], find: A' A(2,3) size(A) LA(:,2)=[] Inv(A)

A: We can solve this as follows: