Multiplying a Matrix by a Vector Worksheet with Answer Key

What's on the worksheet

1. Let A = \begin{bmatrix} -3 & 5 & -4 & -1 \\ -4 & 3 & 3 & 3 \\ 2 & -2 & -4 & 3 \end{bmatrix}, \qquad \mathbf{x} = \begin{bmatrix} -3 \\ 3 \\ 3 \\ -3…
2. A matrix A has A\mathbf{e}_1 = \begin{bmatrix} 1 \\ 0 \\ 2 \\ -1 \end{bmatrix}, \qquad A\mathbf{e}_2 = \begin{bmatrix} 3 \\ 1 \\ 0 \\ 2…
3. A 2 × 3 matrix A satisfies Au = (-2, 5) and Av = (-4, 1), where u = (2, 1, -3) and v = (1, 2, 2).
4. Naomi's gift-basket shop sells three basket styles.
5. Let A = \begin{bmatrix} 1 & 2 & -1 & 3 \\ 2 & 5 & 0 & 4 \\ -1 & -1 & 3 & -5 \end{bmatrix}.
6. Let A and B be m × n matrices.