Question

What is the product?

Answer 1

For this case we have a matrix product:

By definition, are two matrices A and B, to find the product given by the matrix C, it is fulfilled that:

`A_ {m * n} * B_ {n * p} = C_ {m * p}`

So, be the following matrices:

`A_(2*3)=\left[\begin{array}{ccc}1&3&1\\-2&1&0\end{array}\right]\\B_(3*2)=\left[\begin{array}{ccc}2&-2\\3&5\\4&1\end{array}\right]`

We want to find C, given by:

`C_(2*2)=\left[\begin{array}{ccc}1&3&1\\-2&1&0\end{array}\right] *\left[\begin{array}{ccc}2&-2\\3&5\\4&1\end{array}\right]\\C_(2*2)=\left[\begin{array}{ccc}(1*2+3*3+1*4)&(1*-2+3*5+1*1)\\(-2*2+1*3+0*4)&(-2*-2+1*5+0*1)\\\end{array}\right] \\C_(2*2)=\left[\begin{array}{ccc}15&14\\-1&9\\\end{array}\right]`

Answer:

`C_(2*2)=\left[\begin{array}{ccc}15&14\\-1&9\\\end{array}\right]`