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Calculus and Beyond Homework Help
Find all 2x2 matrices X such that AX=XA for all 2x2 matrices
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[QUOTE="Clandry, post: 4990396, member: 442666"] [h2]Homework Statement [/h2] Find all 2x2 matrices X such that AX=XA for all 2x2 matrices[h2]The Attempt at a Solution[/h2] Let A = a b c d and X = w x y z Then AX = XA ==> aw+by=wa+xc ...(1) ax+bz=wb+xd ...(2) cw+dy=ya+zc ...(3) cx+dz=yb+zd ...(4) (1) ==> by = xc, which holds for all b and c only if x=y=0. (2) ==> bz = wb, which hods for all b only if z=w. (3) ==> w=z (4) ==> x=y=0 So the answer is x=y=0, and w=z. That is, X = k*I with k being any real number and I is the identity matrix. How does this look? [/QUOTE]
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Calculus and Beyond Homework Help
Find all 2x2 matrices X such that AX=XA for all 2x2 matrices
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