(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let B be a fixed n x n matrix, and let X_B = { A e M_n so that AB = BA }. In other words, X_B is the set of all matrices which commute with B.

(a) Prove that X_B is a subspace of M_n.

(b) Let B =

[

1 0

2 -1

]

Find a basis for X_B and write its dimension.

(c) Is your basis in part (b) orthogonal? If not, make it orthogonal using the

Gram-Schmidt algorithm. Then, normalize the basis to make it orthonor-

mal.

2. Relevant equations

A e M_n ---> A belongs to set M_n

3. The attempt at a solution

For part (a) what is M_n ? Is this some general notation for a certain matrix (like I for identity)? I think I need to know that before I can try proving anything. Thanks

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# Homework Help: Subspace and basis problem

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