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=

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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=
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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