System of equations ( Modulo )

Question

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Hello everyone. I solved this system, but I dont know how to collect the answers. So I got:

(x_1 -x_2 -x_3 = 0) (0 -2x_2 0 = 0) (0 0 x_3 = 0) in matrix. x_3=x_2=x_1 = 0 I got. But there is one solution. x_1 = x_3 = 1. x_2=0. But how can I see it? Modulo 2

@SiongThyeGoh Thank u! Can I ask u one question? If I want to find the Basis of this system, it will be only (1,0,1)? Because (0,0,0) is linear depend, isnt? — nikibiki, Dec 14 '21 at 07:23

score 1 · Answer 1 · answered Dec 14 '21 at 07:17

1

From the last equation we know that $x_1=x_3$. Using this information, $x_2=0$ from the first two equations.

Hence, we reduce the system to $x_2=0$ and $x_1=x_3$.

The two solutions are $(1,0,1)$ and $(0,0,0)$.

answered Dec 14 '21 at 07:17

Siong Thye Goh

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Thank u! Can I ask u one question? If I want to find the Basis of this system, it will be only (1,0,1)? Because (0,0,0) is linear depend, isnt? – nikibiki Dec 14 '21 at 07:22
Yes. Btw, you might like to read up on Gaussian elimination. – Siong Thye Goh Dec 14 '21 at 07:36

System of equations ( Modulo )

1 Answers1