et 8- ((1, 2), (-1,-1)) and 8- ((-4, 1), (0, 2)) be bases for R², and let A-83] А we the matrix for T: R2 R2 relative to 8. (a) Find the transition matrix P from 8' to 8. P= (b) Use the matrices P and A to find [v]s and [7(v)le, where [v]-[-34). (vla- [T(V)]a- p-1. A'= x (c) Find P-1 and A' (the matrix for T relative to 8). X -1/4 12 1/8 10 -1/2 9/4 1/2 -1/2 x (d) Find (T(v)la two ways. [T()le-P¹[T(v)le- -5/2 19/4
et 8- ((1, 2), (-1,-1)) and 8- ((-4, 1), (0, 2)) be bases for R², and let A-83] А we the matrix for T: R2 R2 relative to 8. (a) Find the transition matrix P from 8' to 8. P= (b) Use the matrices P and A to find [v]s and [7(v)le, where [v]-[-34). (vla- [T(V)]a- p-1. A'= x (c) Find P-1 and A' (the matrix for T relative to 8). X -1/4 12 1/8 10 -1/2 9/4 1/2 -1/2 x (d) Find (T(v)la two ways. [T()le-P¹[T(v)le- -5/2 19/4
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.3: Properties Of Determinants
Problem 63E: Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.
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