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:
[tex]A_ {m * n} * B_ {n * p} = C_ {m * p}[/tex]
So, be the following matrices:
[tex]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][/tex]
We want to find C, given by:
[tex]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][/tex]
Answer:
[tex]C_{2*2}=\left[\begin{array}{ccc}15&14\\-1&9\\\end{array}\right][/tex]
