# If A=((-3, x),(2y, 0)) and B=((4, 6),(-3, 1)), what is A-B?

Mar 10, 2018

$A - B = \left(\begin{matrix}- 7 & x - 6 \\ 2 y + 3 & - 1\end{matrix}\right)$

#### Explanation:

In a matrix problem like this, all you have to do is subtract each element of $B$ from the corresponding element in $A$.

In other words,

$\left(\begin{matrix}- 3 & x \\ 2 y & 0\end{matrix}\right) - \textcolor{b l u e}{\left(\begin{matrix}4 & 6 \\ - 3 & 1\end{matrix}\right)}$

is the same thing as

$\left(\begin{matrix}- 3 - \textcolor{b l u e}{4} & x - \textcolor{b l u e}{6} \\ 2 y - \left(\textcolor{b l u e}{- 3}\right) & 0 - \textcolor{b l u e}{1}\end{matrix}\right)$

Simplifying each statement gives us our answer.

$\left(\begin{matrix}- 7 & x - 6 \\ 2 y + 3 & - 1\end{matrix}\right)$