Three unknowns, the last TWO rows of the matrix contain ALL zeros.

Question

I'm having trouble figuring out how to get the "generic solution" to this matrix by using Gaussian Method by REF. The answer on the back of the book is: $(x,y,\frac{1}{2}x-\frac{3}{2}y)$. I really don't understand the concept behind this answer so if anyone can help, I'd really appreciate it! thank you. I've attached a photo of the problem.

Welcome to MSE. Please type your questions (using MathJax) instead of posting links to pictures. — José Carlos Santos, Mar 09 '18 at 06:54
@JoséCarlosSantos But that doesn't require down voting the question to -5 — Vishaal Selvaraj, Mar 09 '18 at 07:59

Siong Thye Goh · Answer 1 · 2018-03-09T07:52:10.990

0

$$2x+3y+2z=1$$

and there is no other constraints as $0=0$ trivially holds.

Then $$z=\frac{1-3y-2x}{2}=\frac{1}{2}-x-\frac{3y}{2}$$

Hence, given $x,y$, the $z$ must satisfies $z=\frac{1-3y-2x}{2}=\frac{1}{2}-x-\frac{3y}{2}.$

edited Mar 09 '18 at 07:52

answered Mar 09 '18 at 06:56

Siong Thye Goh

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Three unknowns, the last TWO rows of the matrix contain ALL zeros.

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