- #1

ProfuselyQuarky

Gold Member

- 817

- 527

##10x+24y+2z=-18##

##-2x-7y+4z=6##

##-14x-48y+26z=42##

I turned the system into a matrix so that I could solve it using inverses:

##\begin{bmatrix}

10&24&2\\

-2&-7&4\\

-14&-48&26\\

\end{bmatrix}\cdot

\begin{bmatrix}

x\\

y\\

z\\

\end{bmatrix}=

\begin{bmatrix}

-18\\

6\\

42\\

\end{bmatrix}##

But before I did so, I tried to find the determinant of the matrix to see whether ##|A|\neq 0## or not.

##|A|=10

\begin{vmatrix}

-7&4\\

-48&26\\

\end{vmatrix}-24

\begin{vmatrix}

-2&4\\

-14&26\\

\end{vmatrix}+2

\begin{vmatrix}

-2&-7\\

-14&-48\\

\end{vmatrix}=0

##

The matrix is singular, so that means that the system doesn't have a unique solution. The problem was multiple choice, and there was no option for "infinite number of solutions", so I picked "no solution" (badly written multiple choice question, imo). The solution that was posted said that there was, in fact a unique solution:

##

\left\{

\begin{array}{ll}

x=22\\

y=-10\\

z=-5

\end{array}

\right.

##

I've tried to understand what's going on, but I can't figure out why there's a solution.