1. ## Matrix Multiplication

So this is basically the question, and I thought I had it figured out most of the way and hit a bump.
I assumed basically the question was x,y,z multiplied by -5,2,-1 would have to give me zero. So I make that into a matrix and solve x = (5/2)s-(1/5)t
witch would be all fine and dandy, but there are three slots? What am I supposed to put in there?? what a weird question... I was wondering if anyone could give me any insight =) thanks!

2. Originally Posted by melissa727

So this is basically the question, and I thought I had it figured out most of the way and hit a bump.
I assumed basically the question was x,y,z multiplied by -5,2,-1 would have to give me zero. So I make that into a matrix and solve x = (5/2)s-(1/5)t
witch would be all fine and dandy, but there are three slots? What am I supposed to put in there?? what a weird question... I was wondering if anyone could give me any insight =) thanks!
If you let $\displaystyle v=\begin{bmatrix} x & y & z\end{bmatrix}$ and you dot it with
$\displaystyle \begin{bmatrix} -5 \\ 2 \\ -1 \end{bmatrix}$

You wil get $\displaystyle -5x+2y-z=0$ we set it equal to zero because you want them to be perpendicular.

Now solve this underdetermined system.

Since you have 1 equation and 3 unknows your solution will contain 2 paramters (s & t).

I hope this helps

3. well, that is what I did... but then that only fills up the first line and there are three lines i'd have to fill...

4. You solution to -5x+2y-z=0 will be of the form z= ax+ by for some a and b (which are almost embarassingly easy to find). Any point, then, will be of the form (x, y, ax+ by)= (x, 0, ax)+ (0, y, by)= (1, 0, a)x+ (0, 1, b)y. That's why they have two boxes with three rows in each- you have two vectors, each with three components, each vector multiplying one of the two parameters. I've left the parameters as "x" and "y" but you could, of course, use any letters, even "s" and "t".