1. $\begin{bmatrix} -5 & -5 \\ -1 & 2 \end{bmatrix} \cdot \begin{bmatrix} -2 & -3 \\ 3 & 5 \end{bmatrix} = \begin{bmatrix} (-5)(-2) + (-5)(3) & (-5)(-3) + (-5)(5) \\ (-1)(-2) + (2)(3) & (-1)(-3) + (2)(5) \end{bmatrix} = \begin{bmatrix} 10 - 15 & 15 - 25 \\ 2 + 6 & 3 + 10 \end{bmatrix} = \begin{bmatrix} -5 & -10 \\ 8 & 13 \end{bmatrix}$
2. $\begin{bmatrix} -6 & 2 \\ 1 & 2 \\ 4 & 2 \end{bmatrix} \cdot \begin{bmatrix} -1 & 1 \\ -6 & -4 \\ 4 & 0 \\ 3 & 0 \end{bmatrix}$ is undefined because the number of columns in the first matrix (2) does not equal the number of rows in the second matrix (4).
3. $\begin{bmatrix} -4 & 1 & 6 \end{bmatrix} \cdot \begin{bmatrix} 1 \\ 4 \\ 2 \end{bmatrix} = (-4)(1) + (1)(4) + (6)(2) = -4 + 4 + 12 = 12$
4. $\begin{bmatrix} 6 & -12 \\ 5 & 11 \end{bmatrix} \cdot \begin{bmatrix} -5 & -5 \\ -1 & 2 \end{bmatrix} = \begin{bmatrix} (6)(-5) + (-12)(-1) & (6)(-5) + (-12)(2) \\ (5)(-5) + (11)(-1) & (5)(-5) + (11)(2) \end{bmatrix} = \begin{bmatrix} -30 + 12 & -30 - 24 \\ -25 - 11 & -25 + 22 \end{bmatrix} = \begin{bmatrix} -18 & -54 \\ -36 & -3 \end{bmatrix}$
5. $\begin{bmatrix} 5 & 3 & 5 \\ 1 & 5 & 0 \end{bmatrix} \cdot \begin{bmatrix} -4 & 2 \\ -3 & 4 \\ 3 & -5 \end{bmatrix} = \begin{bmatrix} (5)(-4) + (3)(-3) + (5)(3) & (5)(2) + (3)(4) + (5)(-5) \\ (1)(-4) + (5)(-3) + (0)(3) & (1)(2) + (5)(4) + (0)(-5) \end{bmatrix} = \begin{bmatrix} -20 - 9 + 15 & 10 + 12 - 25 \\ -4 - 15 + 0 & 2 + 20 + 0 \end{bmatrix} = \begin{bmatrix} -14 & -3 \\ -19 & 22 \end{bmatrix}$
6. $\begin{bmatrix} 2 & -5v \end{bmatrix} \cdot \begin{bmatrix} -5u & -v \\ 0 & 6 \end{bmatrix} = (2)(-5u) + (-5v)(0) & (2)(-v) + (-5v)(6) = \begin{bmatrix} -10u & -2v - 30v \end{bmatrix} = \begin{bmatrix} -10u & -32v \end{bmatrix}$
Parent Tip: Review the logic above to help your child master the concept of multiplying matrices worksheet.
