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 =
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
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![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 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5f3a7f3-10c4-4869-906a-40675d8d17a6%2F6209fc8c-26dc-4e4b-a41f-cfaad7f72a3d%2Fugbjgdb_processed.jpeg&w=3840&q=75)
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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