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**mr fantastic** A typical element of W1 is (a3 + a4, a2, a3, a4, a5) (*why*?). One possible basis is therefore {(1, 0, 1, 0, 0), (1, 0, 0, 1, 0), (0, 1, 0, 0, 0), (0, 0, 0, 0, 1)}. Check that it spans and is linearly independent. The dimension of W1 is the number of vectors in its basis ......

A typical element of W2 is (a1, a2, a2, a2, -a1) (*why*?). One possible basis is therefore {(1, 0, 0, 0, -1), (0, 1, ,1 ,1, 0)}. Check that it spans and is linearly independent. The dimension of W2 is the number of vectors in its basis ...