Notes
A matrix is a rectangular array. Size is rows × columns.
- Multiply $AB$ only when $A$'s columns equal $B$'s rows: entry $(i,j)$ is row $i$ of $A$ dotted with column $j$ of $B$.
- Matrix multiplication is usually not commutative.
Practice
A $2\times3$ matrix times a $3\times4$ matrix gives size:
Outer dimensions.
$\begin{bmatrix}1&2\\3&4\end{bmatrix}\begin{bmatrix}1\\1\end{bmatrix}=$
Row 1: $1+2$; row 2: $3+4$.
Can a $2\times3$ matrix be multiplied by a $2\times3$ matrix?
3 columns vs 2 rows.
Ready for more? Take the Unit 4 test.