Matrix Multiplication
Question:
Compute: \[ \begin{bmatrix} 1 & -2 \\ 2 & 3 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ -3 & 2 & -1 \end{bmatrix} \]
Compute: \[ \begin{bmatrix} 1 & -2 \\ 2 & 3 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ -3 & 2 & -1 \end{bmatrix} \]
Solution:
Multiply rows of first matrix with columns of second matrix:
\[ = \begin{bmatrix} 1(1) + (-2)(-3) & 1(2) + (-2)(2) & 1(3) + (-2)(-1) \\ 2(1) + 3(-3) & 2(2) + 3(2) & 2(3) + 3(-1) \end{bmatrix} \] \[ = \begin{bmatrix} 1 + 6 & 2 – 4 & 3 + 2 \\ 2 – 9 & 4 + 6 & 6 – 3 \end{bmatrix} \] \[ = \begin{bmatrix} 7 & -2 & 5 \\ -7 & 10 & 3 \end{bmatrix} \]Final Answer:
\[ \boxed{ \begin{bmatrix} 7 & -2 & 5 \\ -7 & 10 & 3 \end{bmatrix} } \]