Multiplying matrices?

Question

I'm having trouble doing this problem
[1, 2, 12] [3, 4]
[12, 2, 1] [4, 3]
[5, 2]

Can someone give me the step on how to multiply matrice, it'll be really helpful. Thanks. Oh sorry the way problem is, it supposed to be like this 1, 2, 12, 12, 2, 1 * 3, 4, 4, 3, 5, 2

Answer 1

Ok, I think your question is asking how to multiply these two matrices A*B:

A =
[1, 2, 12]
[12, 2, 1]

B =
[3, 4]
[4, 3]
[5, 2]

Ok, so I first will give you my brief explanation and give you a couple links that will help explain further.

My explanation:
Take the first column of the right-hand matrix and multiply/add the terms with the first row of the left-hand matrix (3*1+4*2+5*12 = 71). That gives you the first result in your answer. Then continue multiplying/adding the first column of the right-hand matrix with the second row of the left-hand matrix to give the second result in your answer (one space down). It might help to visualize taking the first column of the right-hand matrix and turning it sideways over top of the left-hand matrix.

Then use the second column of the right-hand matrix and multiply/add your way down the left-hand matrix again. This will give the results for the second column of your answer. And then you could repeat the process if there were more columns in the right-hand matrix.

In this case the answer happens to be:
[71, 34]
[49, 56]

And I got that by doing the calculations in the order explained above:
3*1+4*2+5*12 = 71
3*12+4*2+5*1 = 49
4*1+3*2+2*12 = 34
4*12+3*2+2*1 = 56

So, that is how I do it. There are other algorithms, but this works for me, and I hope the explanation is clear. Check out the first link in the sources to get another explanation in words (they do it a bit differently than I have explained). The second link is a matrix calculator to help check your work.

Good luck.

Answer 2

The first matrix (A) is 2×3
The second one (B) is 3×2
The resulting matrix (C) is 2×2
Let the resulting matrix C in the following form
...... | c11 c12 |
C = | c21 c22 |
then cij = the sum of the product of the corresponing elemnts in the (i) raw in matrix A by the (j) coulmn of (b)
i.e c11 = 1×3 + 2×4 + 12×5 = 71
......c12 = 1×4 + 2×3 + 12×2 = 34
......c21 = 12×3 + 2×4 + 1×5 = 49
......c22 = 12×4 + 2×3 + 1×2 = 56

Answer 3

If they are both 2 rows and 3 columns, you can not multiply them together.