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)

## 3x3 Matrix

### 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.

### 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,

So dot product top row by the first, second and third columns to give you the first row of your matrix:

Similarly dot product the second (middle) row by the first, second and third columns to give your second matrix row:

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.

**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.