Consider the following bases B and B' for some subspace of M2x2(R), the vector space of all 2 by 2 matrices over R. u- {[: :] [:}] [:}} - -{[: :] [: :} [:)]} {[: :]· [: :]. [: :]}- {{: :]· [: :]· [: ']} 0 0 3 4 1 0 1 1 3 1 3 0 3 B B' 2 3 4 3 2 1 0 -8 -6 -1 (a) Find the coordinate matrix of A = 4 relative to the basis B', that is 6 [x(A)]g. (b) Calculate the transition matrix PB→B. (Show steps.] (c) Use part 2(b) to calculate the coordinate matrix of A relative to the basis B. (d) Verify the coordinate matrix obtained in part 2(c).

Consider the following bases B and B' for some subspace of M2x2(R), the vector space of all 2 by 2 matrices over R. u- {[: :] [:}] [:}} - -{[: :] [: :} [:)]} {[: :]· [: :]. [: :]}- {{: :]· [: :]· [: ']} 0 0 3 4 1 0 1 1 3 1 3 0 3 B B' 2 3 4 3 2 1 0 -8 -6 -1 (a) Find the coordinate matrix of A = 4 relative to the basis B', that is 6 [x(A)]g. (b) Calculate the transition matrix PB→B. (Show steps.] (c) Use part 2(b) to calculate the coordinate matrix of A relative to the basis B. (d) Verify the coordinate matrix obtained in part 2(c).

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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Concept explainers

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

Consider the following bases B and B' for some subspace of M2x2(R), the vector space
of all 2 by 2 matrices over R.
-{[: :] [}]- [ :]} «-{{; :]- [; :] [: :}
{[: ].
1 0
3 0
0 1
1
1
3 1
3
0 0
В
B'
2 3
4 3
2 1
0 -8
3 4
-6 -1
(a) Find the coordinate matrix of A =
4
relative to the basis B', that is
6.
[x(A)]g".
(b) Calculate the transition matrix PB→B. [Show steps.]
(c) Use part 2(b) to calculate the coordinate matrix of A relative to the basis B.
(d) Verify the coordinate matrix obtained in part 2(c).

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