Let 8 = {(1, 2). (-1, -1)} and B' = {(-4, 1). (0, 2)} be bases for R2, and let 1 0 A = 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 Pand A to find [v]g and [T(v)]g, where [v]g = [3 -217. -11 [v]g= -23 [T(v)]g= (c) Find P-1 and A' (the matrix for T relative to 5). p-1= A'= (d) Find [T(v)]g two ways. [T(v)]g = A[v]g= I1

Let 8 = {(1, 2). (-1, -1)} and B' = {(-4, 1). (0, 2)} be bases for R2, and let 1 0 A = 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 Pand A to find [v]g and [T(v)]g, where [v]g = [3 -217. -11 [v]g= -23 [T(v)]g= (c) Find P-1 and A' (the matrix for T relative to 5). p-1= A'= (d) Find [T(v)]g two ways. [T(v)]g = A[v]g= I1

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

Let 8 = {(1, 2). (-1, -1)} and B' = {(-4, 1). (0, 2)} be bases for R2, and let
1 0
A =
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 Pand A to find [v]g and [T(v)]g, where
[v]g = [3 -217.
-11
[v]g=
-23
[T(v)]g=
(c) Find P-1 and A' (the matrix for T relative to 5).
p-1=
A'=
(d) Find [T(v)]g two ways.
[T(v)]g = A[v]g=
I1

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