1. Let A be an m ( n matrix and let w be a vector in that satisfies the equation Ax = 0. Show that for any scalar c, the vector cw also satisfies Ax = 0. [That is, show that A(cw) = 0.]
2. Let A be an m x n matrix, and let v and w be vectors in with the property that Av = 0 and Aw = 0. Explain why A(v + w) must be the zero vector. Then explain why A(cv + dw) = 0 for each pair of scalars c and d.

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