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10 Nov 2019
6. Suppose that A is a 4 x 3 matrix. Could the columns of A possibly span R4? Why or why not? (Cite a theorem if necessary.) 7. Let A be a 4x 3 matrix, let y be a vector in R3, and let z be a vector in R4. Suppose Ay z. Prove that the system Ax - 4z is consistent. 8. Find the general solution of the following homogeneous system of equations. Express your answer in parametric vector form. 1 22 2x3 - 6r40 2x1 - 4x2 + 3 + 3x40 9. Suppose Ax - b has a solution. Explain why this solution is unique precisely when Ax 0 has only the trivial solution. (Cite a theorem if necessary.)
6. Suppose that A is a 4 x 3 matrix. Could the columns of A possibly span R4? Why or why not? (Cite a theorem if necessary.) 7. Let A be a 4x 3 matrix, let y be a vector in R3, and let z be a vector in R4. Suppose Ay z. Prove that the system Ax - 4z is consistent. 8. Find the general solution of the following homogeneous system of equations. Express your answer in parametric vector form. 1 22 2x3 - 6r40 2x1 - 4x2 + 3 + 3x40 9. Suppose Ax - b has a solution. Explain why this solution is unique precisely when Ax 0 has only the trivial solution. (Cite a theorem if necessary.)
Nestor RutherfordLv2
19 Jun 2019