(Solution) - a Prove that if A is a symmetric matrix then -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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(a) Prove that if A is a symmetric matrix, then ker A = coker A and mg A = comg A.
(b) Use this observation to produce bases for the four fundamental subspaces associated with

(c) Is the converse to part (a) true?