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Consider the following four 2x2 matrices: Aj = A2 = A3 = and A = Prove that a 2x2 matrix M commutes with any 2x2 matrix if, and only if, M commutes with A1, A2, A3, and A4. That is, given a 2x2 matrix M, show that the following statement holds: ( MA1 = | MA3 = A3M, and MA4 A4M. ALM, MA2 = A2M, MN = NM, for every 2x2 matrix N

Consider the following four 2x2 matrices: Aj = A2 = A3 = and A = Prove that a 2x2 matrix M commutes with any 2x2 matrix if, and only if, M commutes with A1, A2, A3, and A4. That is, given a 2x2 matrix M, show that the following statement holds: ( MA1 = | MA3 = A3M, and MA4 A4M. ALM, MA2 = A2M, MN = NM, for every 2x2 matrix N

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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Consider the following four 2×2 matrices: A1 Го A2 = A3 and A4 = Prove that a 2x2 matrix M commutes with any 2×2 matrix if, and only if, M commutes with A1, A2, A3, and A4. That is, given a 2x 2 matrix M, show that the following statement holds: MA1 = A1M, MA2 = A2M, MN = NM, for every 2x2 matrix N A МА3 — АзМ, and MA, — A,М.
Transcribed Image Text:Consider the following four 2×2 matrices: A1 Го A2 = A3 and A4 = Prove that a 2x2 matrix M commutes with any 2×2 matrix if, and only if, M commutes with A1, A2, A3, and A4. That is, given a 2x 2 matrix M, show that the following statement holds: MA1 = A1M, MA2 = A2M, MN = NM, for every 2x2 matrix N A МА3 — АзМ, and MA, — A,М.
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