3x3 Matrix

rustler

Posted 31 January 2007 - 01:19 PM

Hey, I was wondering how you multiply two 3x3 matrices. Its not so much the fianl answer I am concerned with but the process that is used to gain the answer!

For example, how would you multiply:

Top line: (2 -1 2) (3 -1 3)
Middle Line: (-3 0 1) x (0 2 0)
Bottom Line: (0 1 2) (-1 -2 0)

The Wedge Effect

Posted 31 January 2007 - 02:11 PM

You use the same method as you would for multiplying any other matrices, the rows x columns thing. It's really no different.

rustler

Posted 31 January 2007 - 02:16 PM

yeh but I am not even sure how to do that! Still not sure how I passed that outcom in my NAB!

The Wedge Effect

Posted 31 January 2007 - 02:21 PM

I'll let someone else explain, I'm rubbish at explaining this.

dfx

Posted 31 January 2007 - 02:32 PM

What you're essentially doing when multiplying "row by column" is, if you think back to Highers, taking the dot product . Once you see it that way and you obviously are an expert at the dot product by now, it becomes much easier - well it did for me anyway.

So dot product top row by the first, second and third columns to give you the first row of your matrix: [ (2,-1,2).(3,0,-1) ....... (2,-1,2).(-1,2,-2) ...... (2,-1,2).(3,0,0) ] which gives your first row.

Similarly dot product the second (middle) row by the first, second and third columns to give your second matrix row: [ (-3,0,1).(3,0,-1) .......... (-3,0,1).(-1,2,-2) ......... (-3,0,1).(3,0,0)]

Similarly repeat for the third line.

In fact this isn't just an easy way of remembering it, it is technically true that the dot product is the product of a (1x3) matrix by its transpose, but that's getting technical and let's not do that. So two things to remember, (i) row by column and (ii) dot products. Good luck.

ps: the dots between the dot product are just there as spacers.