A) Assume A is 3x3 zero matrix (with all zero entries). Explain solution set of equation Ax = 0.
B) Create the 2x3 matrix A, not in echelon form, such that solution of Ax = 0 is a line in |R^3. Create the 2x3 matrix B, not in echelon form, such that solution of Ax = 0 is the plane in |R^3.
C) Let A be the m x n matrix, and let v and w be vectors in |R^n with property that Av = 0 and Aw = 0. Describe why A(v+w) should be zero vector. Then describe why A(cv+dw) = 0 for every pair of schalars c and d.