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'