# Matrice Multiplication, can someone check my work?

1. Mar 14, 2012

### Deagonx

1. The problem statement, all variables and given/known data
Its a 3x2 multiplying a 2x2. (3 down 2 across, 3x2) I was gone for the day that my teacher explained it to us, and I am not sure how to do it. I tried, but I want to be sure.

2. Relevant equations
5 2
0 -4 _X_ 3 7
1 6 ___ -2 0

3. The attempt at a solution
18 42
-8 0

Can one of you intellectuals tell me if I got the right answer?

EDIT: I realized I didn't actually tell you what I did. I took the first column of numbers in the first matrix (5, 0, 1), and added together the products of it and the first number in the first column (3). I took the 3 numbers from the second column (2, -4, 6) and added the products of them and the first number in the second column (7). I repeated that with the -2 and the 0.

Last edited: Mar 14, 2012
2. Mar 14, 2012

### scurty

You're not multiplying the matrices correctly. Here is what you should do:

$\left( \begin{array}{cc} a & b\\ c & d\\ e & f \end{array} \right) \cdot \left( \begin{array}{cc} g & h\\ i & j\\ \end{array} \right) = \left( \begin{array}{cc} ag + bi & ah + bj\\ cg + di & ch + dj\\ eg + fi & eh + fj \end{array} \right)$

You have a 3x2 (rows x columns) multiplied by a 2x2 matrix. When multiplying, the "inside" two numbers cancel out and the resulting matrix is the dimensions of the outside numbers. So, for example, a 4x3 matrix multiplied by a 3x1 matrix would yield a 4x1 matrix. The inside numbers MUST match, otherwise it's not valid to multiply them.

Try to redo your problem and see what you come up with!

3. Mar 14, 2012

### Deagonx

This time I got
11 35
8 0
-9 7

Is that right?

4. Mar 14, 2012

### SammyS

Staff Emeritus
The singular of the (plural) word matrices, is the word matrix.

5. Mar 14, 2012

### scurty

That answer looks good! And what Sammy posted is also correct, I didn't catch that any of the times I glanced at the subject.

6. Mar 14, 2012

### Staff: Mentor

And matrice is not a word. Those Romans with their Latin language and weird plurals are to blame. Some other Latin-derived words with the same pluralization rules are appendix, aviatrix (female aviator), and circatrix (scar tissue).

7. Mar 14, 2012

### Deagonx

Well, linguistic debates aside, I checked in the back of the book in the selected answers, and it seems I got it right. Thanks for the help, but I have another problem so I posted another thread.