Question: 1. Find a basis for the subspace U = {a b, a c, c b | a, b, c R } of R 3 .

1. Find a basis for the subspace U = {a b, a c, c b | a, b, c R } of R 3 . Please justify your answer

2. True or False. Justify your answer.

(a) Let U1, U2, U3 be subspaces of M22(R). If V = U1 U2 U3, then dim V = 4.

(b) Let U = Span{1+x, x+x 2} and W = Span{x 2} be subspaces of P2(R). Then, U W = {0}

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