The Transpose and Symmetric Matrices Worksheet with Answer Key

What's on the worksheet

1. A square matrix K is skew-symmetric when K^T = -K.
   \begin{bmatrix} -5 & 6 \\ 6 & 2 \end{bmatrix}\begin{bmatrix} 0 & 4 \\ -4 & 0 \end{bmatrix}\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}\begin{bmatrix} 0 & 2 \\ -2 & 0 \\ 1 & 3 \end{bmatrix}\begin{bmatrix} 1 & 3 \\ -3 & 1 \end{bmatrix}
2. Let A = \begin{bmatrix} -2 & -3 & 1 \\ -3 & 4 & 4 \end{bmatrix}, \qquad B = \begin{bmatrix} 1 & 3 \\ 1 & -2 \\ -3 & 1 \end{bmatrix}.
3. A 2 × 3 matrix A is not shown.
4. The columns a_1, a_2, a_3 of a 4 × 3 matrix A are not shown, but you are told A^T A = \begin{bmatrix} 9 & 0 & -3 \\ 0 & 4 & 2 \\ -3 & 2 & 6…
5. Let A = \begin{bmatrix} -2 & 2 \\ -3 & -1 \\ -3 & 1 \end{bmatrix}, \qquad B = \begin{bmatrix} 1 & 1 \\ 3 & 1 \\ -2 & -3 \end{bmatrix}.
6. Jasmine, Jin, Carlos and Aisha, players 1 to 4, play games of table tennis against each other at their club, and every game has a winner.
7. Let A be an n × n matrix and x a column in R^n.