Matrix Multiplication

$$\[ \left( \begin{array}{cc}
1 & 2 \\
3 & 4
\end{array} \right)
%
\left( \begin{array}{cc}
2 & 6 \\
-1 & 0
\end{array} \right)=
%
\left( \begin{array}{cc}
0 & 6 \\
2 & 18
\end{array} \right)
\]
\[ \left( \begin{array}{cc}
0 & 6 \\
2 & 18
\end{array} \right)+
%
\left( \begin{array}{cc}
2 & 6 \\
-1 & 0
\end{array} \right)=
%
\left( \begin{array}{cc}
0 & 12 \\
1 & 18
\end{array} \right)
\]$$

I've never done that before - I'm quite pleased with myself!

You just add the ones that are in the same position.

so would that be..

AB= 0 2     +   B= 2 6

      6 18              -1 0

Hang on I'm trying to work out how to do matrix input.    Ummm

i do it like

AB11= 1X2, 2X-1 = 0

AB12= 1X6, 2X0  = 6

AB21= 3X2, 4X-1 = 2

AB22=-3X6 4X0 = 18

So im just wondering if i put it   0(AB11)   2(AB21)

                                              6(AB12)   18(AB22)

Thanks for the thumbs up 

Thanks for the help! Appreciate it Melody! 

Good job, Melody......you're exactly correct with the nultiplication........

Note that it is easy to remember how to find a paricular element in matrix multiplication. To find element a_ij in the resultant matrix, we just multiply the "ith" row of the first matrix times the "jth" column of the second!!

$$\\A=\left(
\begin{array}{cc}1 & 2 \\3 & 4
\end{array}
\right)\qquad
B=\left(
\begin{array}{cc}2 & 6 \\-1 & 0
\end{array}
\right)$$

$$\boxed{AB+B=(A+\textcolor[rgb]{0,0,1}{I})B}$$

$$\mbox{Identity Matrix }\textcolor[rgb]{0,0,1}{I=\left(
\begin{array}{cc}1 & 0 \\0 & 1
\end{array}
\right)}\\$$

$$\mbox{A+\textcolor[rgb]{0,0,1}{I}} =\left(
\begin{array}{cc}1 & 2 \\3 & 4
\end{array}
\right)
+
\textcolor[rgb]{0,0,1}{\left(
\begin{array}{cc}1 & 0 \\0 & 1
\end{array}
\right)}
}
=
\left(
\begin{array}{cc}1+\textcolor[rgb]{0,0,1}{1} & 2+\textcolor[rgb]{0,0,1}{0} \\3+\textcolor[rgb]{0,0,1}{0} & 4+\textcolor[rgb]{0,0,1}{1}
\end{array}
\right)
=
\left(
\begin{array}{cc}2 & 2 \\3 & 5
\end{array}
\right)$$

$$\mbox{(A+\textcolor[rgb]{0,0,1}{I})B}=\left(
\begin{array}{cc}2 & 2 \\3 & 5
\end{array}
\right)
}
\left(
\begin{array}{cc}2 & 6 \\-1 & 0
\end{array}
\right)
=
\left(
\begin{array}{cc}\textcolor[rgb]{1,0,0}{2} & 12 \\1 & 18
\end{array}
\right)$$

$$\boxed{AB+B=
\left(
\begin{array}{cc}\textcolor[rgb]{1,0,0}{2} & 12 \\1 & 18
\end{array}
\right)
}$$

I'm always impressed with your ability to use LaTex, heureka !!!   ......I wish I could learn that, but I'm probably too old !!!!

Hi Melody,

0 + 2 = 2    n o t  0

Thank you Heureka.

I got that. Back to kindergarten for me!