Let M = -6 - [31] 0 be a vector in the vector space V of 2 × 2 matrices with real number entries. Let C = - [1 0 - 96 J} ] [ be an ordered basis for V. a. Write M as a linear combination of elements of C. -6 - = 3 0 [1 Го + + [1 0 [] [+ 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 =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let
M =
-6
-
[31]
0
be a vector in the vector space V of 2 × 2 matrices with real number entries. Let
C =
-
[1 0
-
96 J}
] [
be an ordered basis for V.
a. Write M as a linear combination of elements of C.
-6
-
=
3
0
[1
Го
+
+
[1 0
[]
[+
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 M = -6 - [31] 0 be a vector in the vector space V of 2 × 2 matrices with real number entries. Let C = - [1 0 - 96 J} ] [ be an ordered basis for V. a. Write M as a linear combination of elements of C. -6 - = 3 0 [1 Го + + [1 0 [] [+ 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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