Linear AlgebraI need help with D 6.45.pls help (c) Find P-1 and A' (the matrix for T relative to B').1111A' =-111(d) Find [T(V)]g two ways.[T(V)]g = P[T(v)]; =[T(V)]g = A'[V]g = Let B = {(0, 1, 1), (1, 1, 0), (1, 0, 1)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R3, and let-1221A =211.be the matrix for T: R3 → R3 relative to B.(a) Find the transition matrix P from B' to B.|-1/21/21/21/21/2-1/2P =1/2-1/21/2(b) Use the matrices P and A to find [V]g and [T(v)]g, where[V]g, = [-1 1 0]".B'1[V]g =-12-3[T(V)]g =

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(c) Find P-1 and A' (the matrix for T relative to B'). 1 1 p-1 = 1 1 1 1

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.4: Transistion Matrices And Similarity

Problem 15E

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Question

Linear Algebra

I need help with D

6.4

pls help

(c) Find P-1 and A' (the matrix for T relative to B').
1
1
1
1
A' =
-1
1
1
(d) Find [T(V)]g two ways.
[T(V)]g = P[T(v)]; =
[T(V)]g = A'[V]g =

Let B = {(0, 1, 1), (1, 1, 0), (1, 0, 1)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R3, and let
-1
2
2
1
A =
2
1
1.
be the matrix for T: R3 → R3 relative to B.
(a) Find the transition matrix P from B' to B.
|-1/2
1/2
1/2
1/2
1/2
-1/2
P =
1/2
-1/2
1/2
(b) Use the matrices P and A to find [V]g and [T(v)]g, where
[V]g, = [-1 1 0]".
B'
1
[V]g =
-1
2
-3
[T(V)]g =

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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