1. Determine whether each of the following statements is True or False. (No justification necessary.) (a) If a matrix equation Ax = b has more than one solution, then the matrix equation Ax = 0 must...

Extracted text: 1. Determine whether each of the following statements is True or False. (No justification necessary.) (a) If a matrix equation Ax = b has more than one solution, then the matrix equation Ax = 0 must also have more than one solution. (b) If A is a 3 x 3 matrix and the matrix equation Ax has a unique solution, then A must be invertible. (c) If A is a 2 x 2 matrix, det A = 2, and B = A², then det 2B = 8. (d) Row operations on a matrix can change its null space. (e) If A is a diagonalizable matrix, then the columns of A must be linearly independent.