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

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

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.1: Operations With Matrices

Problem 77E

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