Linear algebra: please solve both parts correctly and handwritten also write the problem number before start the question Problem 3(1) Let A be an x n-matrix. Define CA to be the set of n x n-matrices that commutewith A i.e.CA = {BЄ Mnxn, B. A = A. B}.Show that CA is a vector subspace of the space Mnxn of n x n-matrices, which is,in addition, closed under matrix multiplication i.e. for any B,C ECA, B. CECA.hint: use the rules (for example Theorem 2.11 in the notes or Theorem 2 in Chap 2.1 ofyour textbook) of matrix multiplication(2) Let A =[]. Determine (find a spanning set of) CA-hint: under which conditions does a matrix [] commute with A?-7 3-51

Problem 3**(1) Let A be an n×n-matrix. Define CA to be the set of n x n-matrices that commute with…

Answered: Problem 3 (1) Let A be an x n-matrix.…

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: please solve both parts correctly and handwritten also write the problem number before start the question

Problem 3
(1) Let A be an x n-matrix. Define CA to be the set of n x n-matrices that commute
with A i.e.
CA = {BЄ Mnxn, B. A = A. B}.
Show that CA is a vector subspace of the space Mnxn of n x n-matrices, which is,
in addition, closed under matrix multiplication i.e. for any B,C ECA, B. CECA.
hint: use the rules (for example Theorem 2.11 in the notes or Theorem 2 in Chap 2.1 of
your textbook) of matrix multiplication
(2) Let A =[]. Determine (find a spanning set of) CA-
hint: under which conditions does a matrix [] commute with A?
-7 3-51

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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