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Let -3 -1 M = -5 1 be a vector in the vector space V of 2 x 2 matrices with real number entries. Let [1 C = be an ordered basis for v . a. Write M as a linear combination of elements of C. -3 -1 [1 Го + + + -5 1 1 b. Let [M]c denote the coordinate representation of M relative to the basis C. Find the coordinate vector representation for M relative to the basis C. Your answer should be a vector of the general form <1,2,3,4>. [M]c =

Let -3 -1 M = -5 1 be a vector in the vector space V of 2 x 2 matrices with real number entries. Let [1 C = be an ordered basis for v . a. Write M as a linear combination of elements of C. -3 -1 [1 Го + + + -5 1 1 b. Let [M]c denote the coordinate representation of M relative to the basis C. Find the coordinate vector representation for M relative to the basis C. Your answer should be a vector of the general form <1,2,3,4>. [M]c =

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.1: Orthogonality In Rn
Problem 10EQ: In Exercises 7-10, show that the given vectors form an orthogonal basis for2or3. Then use Theorem...
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Let -3 M 1 be a vector in the vector space V of 2 x 2 matrices with real number entries. Let [1 0] [1 01 [o C = be an ordered basis for v. a. Write M as a linear combination of elements of C. -3 -1] [1 ГО 1] [1 |-5 + -1 1 Го -1] b. Let [M]c denote the coordinate representation of M relative to the basis C. Find the coordinate vector representation for M relative to the basis C. Your answer should be a vector of the general form <1,2,3,4>. [M]c=
Transcribed Image Text:Let -3 M 1 be a vector in the vector space V of 2 x 2 matrices with real number entries. Let [1 0] [1 01 [o C = be an ordered basis for v. a. Write M as a linear combination of elements of C. -3 -1] [1 ГО 1] [1 |-5 + -1 1 Го -1] b. Let [M]c denote the coordinate representation of M relative to the basis C. Find the coordinate vector representation for M relative to the basis C. Your answer should be a vector of the general form <1,2,3,4>. [M]c=
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