User:

Matrix multiplication

The multiplication of matrices is defined between two matrices only if the number of columns of the first matrix is the same as the number of rows of the second matrix, that is, you can multiply Amxn and Bpxq only when n=p (the result it will be a mxq matrix).

For Amxn and Bnxp, the product of both of them is A·B=C, where C is:
$\fs2c_{ij}=\sum_{k=1}^na_{ik}\cdot\;b_{kj}$
That is, cij=ai1·b1j+ai2·b2j+...+ain·bnj

$\left(\begin{matrix}a&b\\c&dnd{matrix}\right)\cdot\left(\begin{matrix}w&x\\y&znd{matrix}\right)=\left(\begin{matrix}aw+by&ax+bz\\cw+dy&cx+dznd{matrix}\right)$

$\left(\begin{matrix}4&0\\1&8nd{matrix}\right)\cdot\left(\begin{matrix}0&-2\\2&3nd{matrix}\right)=\left(\begin{matrix}4\cdot0+0\cdot2&4\cdot(-2)+0\cdot3\\1\cdot0+8\cdot2&1\cdot(-2)+8\cdot3nd{matrix}\right)=\left(\begin{matrix}0&-8\\16&22nd{matrix}\right)$
$\left(\begin{matrix}0&-2\\2&3nd{matrix}\right)\cdot\left(\begin{matrix}4&0\\1&8nd{matrix}\right)=\left(\begin{matrix}0\cdot4+(-2)\cdot1&0\cdot0+(-2)\cdot8\\2\cdot4+3\cdot1&2\cdot0+3\cdot8nd{matrix}\right)=\left(\begin{matrix}-2&-16\\11&24nd{matrix}\right)$

Calculate:

 $\left[\begin{matrix}-3&4&-3nd{matrix}\right]\left[\begin{matrix}-2\\3\\-1nd{matrix}\right]=$