Consider the following system of linear equations: 1+2x2+3x3 + 4x4 = 0, 4x1+5x2+6x3+7x4 = 0, and...

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Consider the following system of linear equations: 1+2x2+3x3 + 4x4 = 0, 4x1+5x2+6x3+7x4 = 0, and 6x1+7x2+8x3+9x4 = 0. (a) (12 pts) Find a basis for the column space of the coefficient matrix of this system. (b) (8 pts) Find a basis for the solution space of this system. Q2: (a) (10 pts) Find a nonsingular 3 3 matrix A satisfying A4 = ABA+243 [-1 1 -1] where B 0-1 1 0 2-2 (b) (10 pts) Find the inverse of A. Consider the following system of linear equations: 1+2x2+3x3 + 4x4 = 0, 4x1+5x2+6x3+7x4 = 0, and 6x1+7x2+8x3+9x4 = 0. (a) (12 pts) Find a basis for the column space of the coefficient matrix of this system. (b) (8 pts) Find a basis for the solution space of this system. Q2: (a) (10 pts) Find a nonsingular 3 3 matrix A satisfying A4 = ABA+243 [-1 1 -1] where B 0-1 1 0 2-2 (b) (10 pts) Find the inverse of A.