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Let A, B, C square matrices of size 3 x 3. Find a counterexample to the following statements (you can start using matlab): (a) If AC = BC then A = B (b) (A+B)² = A² + 2AB + B². (c) If AB = 0 then A = 0 or B = 0.

Let A, B, C square matrices of size 3 x 3. Find a counterexample to the following statements (you can start using matlab): (a) If AC = BC then A = B (b) (A+B)² = A² + 2AB + B². (c) If AB = 0 then A = 0 or B = 0.

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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Let A, B, C square matrices of size 3 x 3. Find a counterexample to the following statements (you can start using matlab): (a) If AC = BC then A = B (b) (A+B)² = A² + 2AB+ B². (c) If AB = 0 then A = 0 or B = 0. (d) if A² = I3 then A = I3 or A =-I3. I %3D
Transcribed Image Text:Let A, B, C square matrices of size 3 x 3. Find a counterexample to the following statements (you can start using matlab): (a) If AC = BC then A = B (b) (A+B)² = A² + 2AB+ B². (c) If AB = 0 then A = 0 or B = 0. (d) if A² = I3 then A = I3 or A =-I3. I %3D
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