[-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

Question

[-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

loser66 · Answer

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 $\left[\begin{matrix}2\-3\1\end{matrix}\right]$