# Matrix Multipication

roam

## Homework Statement

I look at the following:

$$(x_1\,\,x_2)\begin{pmatrix}1&2\\2&4\end{pmatrix}\binom {x_1}{x_2}=(x_1\,\,x_2)\binom {x_1+2x_2}{2x_1+4x_2}=x_1^2+2x_1x_2+2x_1x_2+4x_2^2$$

And I don't understand how they got from $$(x_1\,\,x_2)\binom {x_1+2x_2}{2x_1+4x_2}$$ to $$x_1^2+2x_1x_2+2x_1x_2+4x_2^2$$.

## The Attempt at a Solution

What process is used here? It surely is not matrix multiplication, otherwise the result would have to be a 1x2 matrix.

Homework Helper
Hi roam!

No, that longy thingy is a 1x2 column.

guerom00
Concerning matrix multiplication, the rule is that a (mxn) matrix multiplied by a (nxp) matrix gives a (mxp) matrix.
Here, you have a (1x2) matrix multiplied by a (2x2) multiplied by a (2x1). Which indeed leeds to a (1x1) matrix i.e. a number.
The part you don't understand is a (1x2) x (2x1) and applying the rules of matrix multiplication you indeed find the result