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E and C= ( Lienly ndependent vectors in he -5 3 The two lists B = of linearly independent vectors in the -2 vector space M2×2 of all 2 × 2 matrices actually both form bases for the same vector subspace V of M2x2- a. Find the change of coordinates matrix from C to B. PBC = b. M is an element of V. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c= [M]B= c. Find M. М —

E and C= ( Lienly ndependent vectors in he -5 3 The two lists B = of linearly independent vectors in the -2 vector space M2×2 of all 2 × 2 matrices actually both form bases for the same vector subspace V of M2x2- a. Find the change of coordinates matrix from C to B. PBC = b. M is an element of V. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c= [M]B= c. Find M. М —

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 7AEXP
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=G 9: and c =<,L rimenly independent vectos in the [-5 3 1 ) and C = of linearly independent vectors in the 3 vector space M2x2 of all 2 x 2 matrices actually both form bases for the same vector subspace V of M2x2. a. Find the change of coordinates matrix from C to B. PB-C= b. M is an element of V. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c= 3 [M]B= c. Find M. M =
Transcribed Image Text:=G 9: and c =<,L rimenly independent vectos in the [-5 3 1 ) and C = of linearly independent vectors in the 3 vector space M2x2 of all 2 x 2 matrices actually both form bases for the same vector subspace V of M2x2. a. Find the change of coordinates matrix from C to B. PB-C= b. M is an element of V. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c= 3 [M]B= c. Find M. M =
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