Consider the matrix A and the vector b. A 1 2 3 1 b = a) Compute the rank of the matrix A. b) Compute the null space of the matrix A and of the matrix AT. c) Compute the least-squares solution of the set of equations Ax = b.

Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of B and the column vectors of AB are in the column space of A.

Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.

Determine if the statement is true or false. If the statement is false, then correct it and make it true. For the product of two matrices to be defined, the number of rows of the first matrix must equal the number of columns of the second matrix.