Question

Use Cramer’s rule to solve for y in the following system of equations.
x + 4y – 2z = 3
x + 3y + 7z = 1
2x + 9y + z = 8

Answer 1

Placing in a matrix,\[\left[\begin{matrix}1 & 4 &-2\\ 1 & 3 & 7 \\ 2 & 9 & 1\end{matrix}\right]\times \left[\begin{matrix}x \\ y \\ z\end{matrix}\right]=\left[\begin{matrix}3 \\ 1 \\ 8\end{matrix}\right]\]\[\det \left[\begin{matrix}1 & 4 &-2\\ 1 & 3 & 7 \\ 2 & 9 & 1\end{matrix}\right]=-14\]Using cramers rule,\[x=\det \left[\begin{matrix}3 & 4 & -2 \\ 1 & 3 & 7 \\ 8 &9 & 1\end{matrix}\right]\div(-14)=70\div(-14)=-5\]\[y=\det \left[\begin{matrix}1 & 3 & -2 \\ 1 & 1 & 7 \\ 2 & 8 & 1\end{matrix}\right]\div(-14)=(-28)\div(-14)=2\]\[z=\det \left[\begin{matrix}1 & 4 & 3 \\ 1 & 3 & 1 \\ 2&9&8\end{matrix}\right]\div(-14)=0\div(-14)=0\]

Cheers!

Answer 2

Thanks A bunch!