Question

Let B = {(1, 3), (-2, -2)} and B' = {(-12, 0), (-4, 4)} be bases for R^2, and let A = [0 3; 4 2] be the matrix for T: R^2 -> R^2 relative to B. (a) Find the transition matrix P from B' to B. P = [6 4; 9 4] (b) Use the matrices P and A to find [v]_B and [T(v)]_B, where [v]_{B'} = [-2 1]^T. [v]_B = [4; -2] [T(v)]_B = [ ; ] (c) Find P^-1 and A' (the matrix for T relative to B'). P^-1 = [ ; ] A' = [ ; ] (d) Find [T(v)]_{B'} two ways. [T(v)]_{B'} = P^-1[T(v)]_B = [ ; ] [T(v)]_{B'} = A'[v]_{B'} = [ ; ]

          Let B = {(1, 3), (-2, -2)} and B' = {(-12, 0), (-4, 4)} be bases for R^2, and let
A = [0 3; 4 2]
be the matrix for T: R^2 -> R^2 relative to B.
(a) Find the transition matrix P from B' to B.
P = [6 4; 9 4]
(b) Use the matrices P and A to find [v]_B and [T(v)]_B, where
[v]_{B'} = [-2 1]^T.
[v]_B = [4; -2]
[T(v)]_B = [ ; ]
(c) Find P^-1 and A' (the matrix for T relative to B').
P^-1 = [ ; ]
A' = [ ; ]
(d) Find [T(v)]_{B'} two ways.
[T(v)]_{B'} = P^-1[T(v)]_B = [ ; ]
[T(v)]_{B'} = A'[v]_{B'} = [ ; ]

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Let B = (1, 3), (-2, -2) and B' = (-12, 0), (-4, 4) be bases for R^2, and let
A = [0 3; 4 2]
be the matrix for T: R^2 -> R^2 relative to B.
(a) Find the transition matrix P from B' to B.
P = [6 4; 9 4]
(b) Use the matrices P and A to find [v]B and [T(v)]B, where
[v]B' = [-2 1]^T.
[v]B = [4; -2]
[T(v)]B = [ ; ]
(c) Find P^-1 and A' (the matrix for T relative to B').
P^-1 = [ ; ]
A' = [ ; ]
(d) Find [T(v)]B' two ways.
[T(v)]B' = P^-1[T(v)]B = [ ; ]
[T(v)]B' = A'[v]B' = [ ; ]

Added by Seth P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

08/30/2023

Step 1

For the first vector in B', (-12, 0), we can write it as a linear combination of the vectors in B: -6(1, 3) + 3(-2, -2) = (-12, 0) For the second vector in B', (-4, 4), we can write it as a linear combination of the vectors in B: 2(1, 3) + 3(-2, -2) = (-4, Show more…

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Let B = {(1, 3), (-2, -2)} and B' = {(-12, 0), (-4, 4)} be bases for R^2, and let A = [0 3; 4 2] be the matrix for T: R^2 -> R^2 relative to B. (a) Find the transition matrix P from B' to B. (b) Use the matrices P and A to find [v]_B and [T(v)]_B, where [v]_{B'} = [-2 1]^T. (c) Find P^-1 and A' (the matrix for T relative to B'). (d) Find [T(v)]_{B'} two ways. [T(v)]_{B'} = P^-1[T(v)]_B [T(v)]_{B'} = A'[v]_{B'}

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