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مشاهدة النسخة كاملة : How can we multiply two matrices together?



A7med Baraka
04-04-2009, 01:16 AM
OK so now we know what shape of matrices can be multiplied together, how do we actually do it?
It seems quite a complicated procedure at first but after some practice you'll find you get used to it. Here's a diagram to illustrate it.
http://www.ucl.ac.uk/Mathematics/geomath/level2/mat/mat71.gif
To start with, we'll concentrate on working out the first element of the result matrix, element a11.(That's the element in the first row and the first column of the result matrix.)
We need to use the first row of the first matrix and the first column of the second matrix.
We work our way across that first row and at the same time down that second column, shown by the lines I've drawn in, multiplying the two elements together.
The first thing to do is to multiply the 1 in the first matrix by the 3 in the second matrix. Then, moving across the top row in the first matrix and down the first column in the second matrix, we multiply the 2 by the 4. Finally we add the results of those two multiplications to get the element a11 in the result matrix.
That gives 1x3+2x4=3+8=11. So the element a11 in the result matrix is 11.
The subscripts in that result element show which row and column we used to find it: we used the first row in the first matrix, that gives the first subscript 1 and we used the first column in the second matrix, that gives the second subscript 1.
We'll go through all the other elements in the result matrix in the same way. Don't worry if it seems confusing now, by the time you've gone through the other 5 elements it will probably be getting clearer!