# How to multiply two matrices?

1. Nov 4, 2007

### transgalactic

how to multiply two matrices??

i cant understand the rule.

where can i find a good manual to explain
how to multiply two matrices?

2. Nov 4, 2007

3. Nov 4, 2007

### HallsofIvy

Staff Emeritus
Do you know how to take the dot product of two vectors?

If so, think of each row of the "left" matrix and each column of the "right" matrix as a vector. The number in the "ith row, jth column" is the dot product of the ith row of the "left" matrix and jth column of the "right" matrix.

4. Nov 4, 2007

### transgalactic

i know dot product from physics when
in rigid bodies i was needed to calculate torqe

i did |a|*|b|*cos(angle between them)

can u give me an example of row and column and how to calculate their dot product?

5. Nov 4, 2007

### robphy

$$\vec F\cdot \vec s = \vec F^\top \vec s= \left[ \begin{array}{lll} F_x & F_y & F_z\ \end{array} \right] \left[ \begin{array}{l} s_x & s_y & s_z \end{array} \right]$$

6. Nov 4, 2007

### Antineutron

I think a demonstration of two square matrices would be more helpful for him. I think he needs a demonstation of a multiplication of a 2x2 matrix, and I'm sure he will have no problems afterwards. Sometimes a good demonstration is needed if the student does not have any experience in matrix multiplication. Sometimes we have to assume that student has no background working out matrix multiplication operations.

7. Nov 4, 2007

### matt grime

What do you mean by 'understand'? Can you follow the 'rule', which is just plugging things into an formula?

8. Nov 4, 2007

### transgalactic

i understood that in order to find a certain object in a matrix
we need to do a dot product of a row of one matrix
and a column of another matrix

can some one give me an example
of how to make this dot product in numbers
with a solution

for example how i make a dot product of column
2
3
4

and row 5 6 7
??

Last edited: Nov 5, 2007
9. Nov 5, 2007

### HallsofIvy

Staff Emeritus
Then I really do feel sorry for you! That's a remarkably difficult definition to use! You will want to learn and use: the dot product of two vectors given in components is
<a b c>.<d e f>= ad+ be+ cf. And it really doesn't matter that they are "row" and "column".

10. Nov 5, 2007

### robphy

Actually torque uses the sin(angle between them).
Since you mentioned dot-product and physics, I thought you would have encountered "work"... which is why I gave my example above in that form.

11. Nov 7, 2007

### transgalactic

thank u all

12. Nov 11, 2007

### Edgardo

Hello transgalactic,

an easy way to multiply matrices is to use the so-called Falk scheme.

1) Here is a video of somebody showing how to use the Falk scheme. It's in German but the calculations
should be self-explanatory.

2) Here is another example. In the example you see the Falk scheme on the right side.
Do you see the 8? You get the 8 by "tilting" the column vector (2,1,1) to the row vector (3,2,0) and forming the dot product.

So in your imagination you have the vector (2,1,1) lying on (3,2,0):
(2,1,1)
(3,2,0)
from which you get: 2*3 + 1*2+1*0 = 8

Do you see the 4 (right to the 8)? You get the 4 by "tilting" the column vector (0,2,3) to the row vector (3,2,0) and forming the dot product.

So in your imagination you have the vector (0,2,3) lying on (3,2,0):
(0,2,3)
(3,2,0)
from which you get: 0*3 + 2*2 + 3*0 = 4