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$$A= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{bmatrix} $$

I'm a bit confused. I got this type of matrix when I was a question regarding eigen values and eigen vectors. This is a $Ax = 0$ matrix btw.

The answer is, $x_1 = 0, x_2 = s, x_3 = 0$. I'm confused because using this logic why is $x_1 = 0$ ? ? When I first did it I got $x_1 = 0, x_2 = 0, x_3 = 0$

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1 Answer 1

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Calculating $Ax=0$ you have the system: $$ \begin{cases} x_1=0\\ x_3=0\\ 0=0 \end{cases} $$

so the solution is a vector that has $x_1=x_3=0$ and the other component ($x_2$) can be any value.

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  • $\begingroup$ Oh so if no value is given we have to assume its any value? Thx $\endgroup$
    – user349557
    Apr 1, 2017 at 7:08
  • $\begingroup$ Yes, $0=0$ is an identity. You can verify by direct substitution that $(0,x_2,0)$ verify the equation $\forall x_2$. $\endgroup$ Apr 1, 2017 at 7:12

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