Question

matrices, concurrent lines and unique solutions
Help with distinguishing them apart

Answer 1

When given this equation:
\[\left[\begin{matrix}2 & -1 &0\\ 2 & 1 & 4 \\ 3 & 0 & 2 \end{matrix}\right] \left(\begin{matrix}x \\ y\\z\end{matrix}\right)=\left(\begin{matrix}0 \\ 0 \\0\end{matrix}\right)\]

The relationship of |M| not equal 0 results in a unique solution.
Now this matrix has a determinant 12 I think, anyway non zero, so should there be a unique solution? answer book says no, x=y=z=0 seems unique to me?

No for concurrent lines to have a solution their determinant = 0
this seems confusing!

Any help much appreciated

Answer 2

anybody?