4 Consider the ordered bases B = ( and -4 3 C = (| -2 1 ) for the vector space V of lower triangular 2 × 2 matrices with -3 3 zero trace. a. Find the transition matrix from C to B. b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is -3 [M]c = [M]B c. Find M. M = ||

4 Consider the ordered bases B = ( and -4 3 C = (| -2 1 ) for the vector space V of lower triangular 2 × 2 matrices with -3 3 zero trace. a. Find the transition matrix from C to B. b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is -3 [M]c = [M]B c. Find M. M = ||

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

4
Consider the ordered bases B
) and
3
C =
1
) for the vector space V of lower triangular 2 × 2 matrices with
-2
-3
3
-
zero trace.
a. Find the transition matrix from C to B.
b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is
-3
[M]c
[M]B
c. Find M.
M

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