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2. Let A € M, (R) be given. (a) If AA = 0n, prove that A = 0₁. Does this hold if A € M₂, (C)? (b) Suppose that A¹A = AA¹. Prove that A¹A = A² if and only if A is symmetric.

2. Let A € M, (R) be given. (a) If AA = 0n, prove that A = 0₁. Does this hold if A € M₂, (C)? (b) Suppose that A¹A = AA¹. Prove that A¹A = A² if and only if A is symmetric.

Advanced Engineering Mathematics
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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2. Let A € M, (R) be given. (a) If AA = 0n, prove that A = 0₁. Does this hold if A € M₂, (C)? (b) Suppose that A¹ A = AA. Prove that A'A= A² if and only if A is symmetric.
Transcribed Image Text:2. Let A € M, (R) be given. (a) If AA = 0n, prove that A = 0₁. Does this hold if A € M₂, (C)? (b) Suppose that A¹ A = AA. Prove that A'A= A² if and only if A is symmetric.
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