- #1

ToastIQ

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Just started with linear algebra Could someone help me with this problem?

\(\displaystyle

2x_1 + x_2 - x_3 + 3x_4 - 3x_5 = 0\\

3x_1 + 2x_2 + x_3 + 2x_4 + 2x_5 = 0\\

-4x_1 + 3x_2 + 2x_3 + x_4 - 4x_5 = 0

\)

(Sorry, I don't know how to do these big brackets for equation systems in Latex.)

So it's a homogeneous system with more unknown variables than equations. I know I'll have to use two parameters. But I just can't get it right. What's the best way to start? Add the first and second equation to eliminate \(\displaystyle x_3 \)?

Answer should be

\(\displaystyle x_1 = -4t_1 - t_2\\x_2 = -35t_1 + 2t_2\\x_3 = 32t_1 - 3t_2\\x_4 = 25t_1\\x_5 = t_2\)