## anonymous one year ago [-4 -1 5] A=[-3 1 9] [3 -3 -15] Observe that the third column of A is -2 times the first column plus 3 times the second column. Use this information to find a nontrivial solution to Ax = 0

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1. Loser66

I don't know how the logic on it. I solve it as usual and get the result (2, -3,1). Then I tried to link to what they hint. $$Column_3 = -2~Column_1+3~Column_2$$, hence $$C_3 + 2C_1-3C_2=0$$ Reorder it , we have $$2C_1- 3C_2 +C_3=0$$ and observe that the coefficient of them is our solution $$\left[\begin{matrix}2\\-3\\1\end{matrix}\right]$$