Question: 4. Given a homogeneous system An: = 0 with three equations and six variables. Suppose a basis for the nullspace of A is given by

4. Given a homogeneous system An: = 0 with three equations and six variables. Suppose a basis for the nullspace of A is given by (i) [4 marks] Find the reduced row echelon form of A. 1 (ii) [2 marks] Suppose is a solution of An: = b for some b E R3. Write 1 down a general solution of An: = b. (iii) [3 marks] True or false: The nonhomogeneous system An: = c is consis tent for every c E R3. Justify your answer. (iv) [3 marks] If B is a 3 X 3 invertible matrix, nd a basis for the nullspaoe of BA. Explain how you derive the

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