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Asked Mar 4, 2020
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Let T and U be linear operators on R2 defined for all (x1, x2) E R2 by T(x1, x2) = (x1, 0) and U(x1, x2) = (x1 + x2, 0).
(a) Prove that (UT)† #TTU†.
(b) Exhibit matrices A and B such that AB is defined, but (AB)†#B†A†.
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Let T and U be linear operators on R2 defined for all (x1, x2) E R2 by T(x1, x2) = (x1, 0) and U(x1, x2) = (x1 + x2, 0). (a) Prove that (UT)† #TTU†. (b) Exhibit matrices A and B such that AB is defined, but (AB)†#B†A†.

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