# Vectors and Matrices problem

#### Malsch

Joined Mar 19, 2011
23
Hi,

I have the following situation: w = px + qy + rz = qi - 5qj - 11pk
where w, x, y and z are vectors and:
x = 4i + 2j - 3k
y = 5i - 3j + 8k
z = -2i - j + 4k

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 #### Tesla23

Joined May 10, 2009
406
Hi,

I have the following situation: w = px + qy + rz = qi - 5qj - 11pk
where w, x, y and z are vectors and:
x = 4i + 2j - 3k
y = 5i - 3j + 8k
z = -2i - j + 4k

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 (0 0 8 | 0) means that r=0
(4 4 -2 | 0) then gives p=-q

so the general solution is (p,q,r) = (a, -a, 0) for any value 'a'