Let -4 M = 3 be a vector in the vector space V of 2 × 2 matrices with real number entries. Let B be an ordered basis for V. 0 0 0 0 0 = { [ ] [ ] [ ] [ ] } a. Write M as a linear combination of elements of B. 4 = 3 -1 [10] 00 Го + + Го 07 10 ] Го + b. Let [M]B denote the coordinate representation of M relative to the basis B. Find the coordinate vector representation for M relative to the basis B. Your answer should be a vector of the general form <1,2,3,4>. [M]B=
Let -4 M = 3 be a vector in the vector space V of 2 × 2 matrices with real number entries. Let B be an ordered basis for V. 0 0 0 0 0 = { [ ] [ ] [ ] [ ] } a. Write M as a linear combination of elements of B. 4 = 3 -1 [10] 00 Го + + Го 07 10 ] Го + b. Let [M]B denote the coordinate representation of M relative to the basis B. Find the coordinate vector representation for M relative to the basis B. Your answer should be a vector of the general form <1,2,3,4>. [M]B=
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 69E: Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of...
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![Let
-4
M =
3
be a vector in the vector space V of 2 × 2 matrices with real number entries. Let
B
be an ordered basis for V.
0 0 0 0 0
= { [ ] [ ] [ ] [ ] }
a. Write M as a linear combination of elements of B.
4
=
3
-1
[10]
00
Го
+
+
Го 07
10
]
Го
+
b. Let [M]B denote the coordinate representation of M relative to the basis B. Find
the coordinate vector representation for M relative to the basis B. Your answer
should be a vector of the general form <1,2,3,4>.
[M]B=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5f3a7f3-10c4-4869-906a-40675d8d17a6%2F8a3e3119-1f7f-4d3c-82d8-a08e649aca70%2Fu8p0p9r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let
-4
M =
3
be a vector in the vector space V of 2 × 2 matrices with real number entries. Let
B
be an ordered basis for V.
0 0 0 0 0
= { [ ] [ ] [ ] [ ] }
a. Write M as a linear combination of elements of B.
4
=
3
-1
[10]
00
Го
+
+
Го 07
10
]
Го
+
b. Let [M]B denote the coordinate representation of M relative to the basis B. Find
the coordinate vector representation for M relative to the basis B. Your answer
should be a vector of the general form <1,2,3,4>.
[M]B=
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