1M2be a vector in the vector space V of 2 × 2 matrices with real number entries. Let0.10.be an ordered basis for V.a. Write M as a linear combination of elements of C.[1 -6'0 10.2 -711b. Let [M]c denote the coordinate representation of M relative to the basis C. Find thecoordinate vector representation for M relative to the basis C. Your answer should be avector of the general form <1,2,3,4>.[M]c

The given matrix is M=1-62-7 The basis of the vector space V are C=1001,0110,100-1,0-110

M be a vector in the vector space V of 2 × 2 matrices with real number entries. Let 0. be an ordered basis for V. a. Write M as a linear combination of elements of C. -6 0 1 0 -1 2 -7 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 = %3D

M be a vector in the vector space V of 2 × 2 matrices with real number entries. Let 0. be an ordered basis for V. a. Write M as a linear combination of elements of C. -6 0 1 0 -1 2 -7 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 = %3D

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

1
M
2
be a vector in the vector space V of 2 × 2 matrices with real number entries. Let
0.
1
0.
be an ordered basis for V.
a. Write M as a linear combination of elements of C.
[1 -6'
0 1
0.
2 -7
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

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