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> Vectors And Matrices Problem
malsch
Posted: December 10, 2011 12:03 pm
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Hi,

I have the following situation: n = 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 smile.gif

This post has been edited by malsch on December 11, 2011 08:50 am
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tashirosgt
Posted: December 10, 2011 04:35 pm
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You could continue the elimination process to get

(4 4 0 | 0)
(0 0 0 | 0)
(0 0 1 | 0)

and

(1 1 0 | 0)
(0 0 0 | 0)
(0 0 1 | 0)

These equations imply that r = 0 and p = -q. So there is an infinite family of solutions. The general form of a solution is (p,q,r) = (a,-a,0) where a is any number.
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