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## anonymous one year ago For the question: Given that the determinant of the 3x3 matrix of (left to right, top to bottom) (a, 1, 1)(b, 2, 1)(c, 3, 1) is -9, find the exact value of x when ax+y+z=1,bx+2y+z=-2 and cx+3y+z=3. I've already figured out from the matrix that -a+2b-c=-9, what should I do now?

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1. anonymous

$\left[\begin{matrix}a & 1 & 1 \\ b & 2 & 1 \\ c & 3 & 1\end{matrix}\right]$

2. anonymous

I think I've worked it out, isn't it just 8/9?

3. mathmate

Yes, 8/9 is correct for x. Cramer's rule?

4. anonymous

Yup, seemed like the only way to work out the question, thanks for the confirmation!

5. mathmate

You're welcome! :)

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