The Invertible Matrix Theorem Worksheet with Answer Key

What's on the worksheet

1. Decide whether each matrix is invertible without row reducing.
2. For a number k, let A_k = \begin{bmatrix} 1 & 2 & 2 \\ 0 & 1 & 2 \\ k & -8 & -10 \end{bmatrix}, with rows r_1, r_2, r_3.
3. Let A = \begin{bmatrix} 1 & 2 & 0 & 1 \\ 0 & 1 & 1 & 2 \\ 2 & 1 & -1 & 0 \\ -1 & 3 & 3 & 5 \end{bmatrix}.
4. A and B are n × n matrices.
5. The 5 × 5 matrix A has one known property:
6. A is a 4 × 6 matrix, and some 6 × 4 matrix D has AD = I_4.