Matrix Multiply
Multiply the two matrices shown:
Expand Hint
Matrix A is a 3-row, 2-column matrix. Matrix B is a 2-row, 2-column matrix. For multiplication to be possible, the number of columns in A must equal the number of rows in B.
Hint 2
Multiplying matrix B by matrix A:
$$$C=\begin{bmatrix}a & b\\ c & d\\ e & f\end{bmatrix}\cdot \begin{bmatrix}h & i\\ j & k\end{bmatrix}=\begin{bmatrix}(a\cdot h+b\cdot j) & (a\cdot i+b\cdot k)\\ (c\cdot h+d\cdot j) & (c\cdot i+d\cdot k)\\ (e\cdot h+f\cdot j) & (e\cdot i+f\cdot k)\end{bmatrix}$$$
Matrix A is a 3-row, 2-column matrix. Matrix B is a 2-row, 2-column matrix. For multiplication to be possible, the number of columns in A must equal the number of rows in B. Multiplying matrix B by matrix A:
$$$C=\begin{bmatrix}a & b\\ c & d\\ e & f\end{bmatrix}\cdot \begin{bmatrix}h & i\\ j & k\end{bmatrix}=\begin{bmatrix}(a\cdot h+b\cdot j) & (a\cdot i+b\cdot k)\\ (c\cdot h+d\cdot j) & (c\cdot i+d\cdot k)\\ (e\cdot h+f\cdot j) & (e\cdot i+f\cdot k)\end{bmatrix}$$$
Thus,
$$$\begin{bmatrix}0 & 5\\ 1 & 10\\ 2 & 3\end{bmatrix} \cdot \begin{bmatrix}-1 & -2\\ 1 & -3\end{bmatrix}= \begin{bmatrix}(0\cdot (-1)+5\cdot 1) & (0\cdot (-2)+5\cdot (-3))\\ (1\cdot (-1)+10\cdot 1) & (1\cdot (-2)+10\cdot (-3))\\ (2\cdot (-1)+3\cdot 1) & (2\cdot (-2)+3\cdot (-3))\end{bmatrix}$$$
$$$= \begin{bmatrix}(0+5) & (0-15)\\ (-1+10) & (-2-30)\\ (-2+3) & (-4-9)\end{bmatrix}=\begin{bmatrix}5 & -15\\ 9 & -32\\ 1 & -13\end{bmatrix}$$$
$$$\begin{bmatrix}5 & -15\\ 9 & -32\\ 1 & -13\end{bmatrix}$$$
Time Analysis
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