I have the following situation:

**w**= p

**x**+ q

**y**+ r

**z**= q

**i**- 5q

**j**- 11p

**k**

where w, x, y and z are vectors and:

**x**= 4

**i**+ 2

**j**- 3

**k**

**y**= 5

**i**- 3

**j**+ 8

**k**

**z**= -2

**i**-

**j**+ 4

**k**

i need to find all the possible values of p, q and r.

I substituted x, y and z in the first equation and compared coefficients of i, j and k and ended up with the following equations:

4p + 4q - 2r = 0

2p + 2q - r = 0

8p + 8q +4r = 0

This implies that one solution is obviously 0 for all the 3 unknowns. I really do not know how to continue from here. i used gaussian elimination and ended up with the following matrix:

(4 4 -2 | 0)

(0 0 0 | 0)

(0 0 8 | 0)

Any help would be greatly appreciated. 10q