Help with matrices...please?

Question

how do you multiply matrices with different dimensions?
one is
0 1
1 0


the other is
-2 -1 2 2
1 3 2 -1

(those are all one digit numbers)

and to the rude people out there.....i TRIED to do this...but i missed this day in class ...thanks a lot for giving your opinion on something you dont know anything about.

Answer 1

You can only multiply matrices when the number of columns of the first matrix equals the number of rows of the second (which these do.)

The resulting matrix will have the # of rows of the first matrix and the # of columns of the second.

To get the number in the first row, first column (shorthand- 1,1) of your resulting matrix:
you use the first row of the first matrix and the second column of the second matrix.
1. Multiply the number in position (1,1) of the first matrix (which is 0) by the number in position (1,1) of the second matrix (which is -2.)
2. Multiply (1,2) of matrix 1 (which is 1) by (2,1) of matrix 2 (which is 1)
3. Add these two products together.

You now have the first entry in your matrix!

To get the other numbers, find the location of where it will be in the matrix [(1,2) will be the entry next to the first one] and use the corresponding row from matrix 1 and the corresponding column from matrix 2.

Let me know if you need more help.

Answer 2

It's normally MUCH easier to use technology (a graphing calculator) when multiplying matrices, but you can do them by hand. What you do is to take each row of the first matrix and each column of the second matrix. You match up the numbers (first with first and second with second), and then you multiply them and add.

The example you have would be:

0*-2 + 1*1 0*-1 + 1*3 0*2+1*2 0*2 + 1*-1
1*-2 + 0*1 1*-1 + 0*3 1*2+0*2 1*2 + 0*-1

which is

1 3 2 -1
-2 -1 2 2

Your answer will always have the number of rows from the first matrix and the number of columns from the second.

Again, for each entry in the answer, you take the corresponding row from the first matrix and column from the second. Multiply the entries that match up, and then add them together.

Answer 3

In order to multiply matrices, the inside dimensions have to be the same. Your first is 2x2, the second is 2x4. The first number represents rows, the second is columns. Since the inside 2's match they can be multiplied. The 2 and 4 on the outside tell you how big the result will be. So draw a space for a 2x4 matrix.

Starting with the zero in the upper left corner, you'll multiply and add to find your first number. 0(-2) + 1(1) = 1. The numbers in the first ROW of the first matrix combine with the numbers in the first COLUMN of the second matrix. The answer goes in the first spot in your new matrix.

Then combine the first row of the first matrix with the second column of the second matrix. 0(-1) + 1(3) = 3. This answer goes in the first row second column of the new matrix.

It's hard to put the whole thing here. Try this website:

www.sosmath.com/matrix/matrix1/matrix1.html

Answer 4

it will be like
(0)*(-2)+1(1) (0)(-1)+(1)(3) (0)(2)+(1)(2) (0)(2)+(1)(-1)
(1)(-2)+(0)(1) (1)(-1)+(0)(3) (1)(2)+(0)(2) (1)(2)+(0)(-1)

1 3 2 -1
-2 -1 4 1