First, we have to make sure that the number of columns in the first matrix is equal to the number of rows in the second matrix.
[tex] \left[\begin{array}{cc}1&-3&2&0\\\end{array}\right] * \left[\begin{array}{ccc}2&3&4\\1&2&3\end{array}\right] [/tex]
Since this is true, we can continue to solve the problem.
To multiply two matrices, multiply each row element in the first matrix by each column element in the second matrix. For example:
1*2 = 2
-3*1=-3
Then we add them to get our new matrix element.
-3+2=-1
Then we move to the next column of the second matrix.
1*3=3
-3*2=-6
-6+3=-3
Then the final column of the second matrix.
1*4=4
-3*3=-9
-9+4=-5
Our matrix so far:
[tex] \left[\begin{array}{ccc}-1&-3&-5\\x&x&x\end{array}\right] [/tex]
We do the same for the bottom row of the first matrix.
First Column
2*2=4
0*1=0
4+0=4
Second Column
2*3=6
0*2=0
6+0=6
Third Column
2*4=8
0*3=0
8+0=8
Our final matrix is:
[tex]\left[\begin{array}{ccc}-1&-3&-5\\4&6&8\end{array}\right][/tex]
:)
