Matrice Multiplication, can someone check my work?

[Deagonx]

Homework Statement

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.

Homework Equations

5 2
0 -4 _X_ 3 7
1 6 ___ -2 0

The Attempt at a Solution

The answer I got was
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.

 

[scurty]

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

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

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!

 

[Deagonx]

This time I got
11 35
8 0
-9 7

Is that right?

 

[SammyS]

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

 

[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.

 

[Mark44]

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

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).

 

[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.