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Q.
The system of equations $3x + y - z = 0 $
$5x + 2y - 3z = 2$
$15x + 6y - 9z = 5 $ has
Matrices
Solution:
$ \Delta = \begin{vmatrix}3&1&-1\\ 5&2&-3\\ 15&6&-9\end{vmatrix}=3\begin{vmatrix}3&1&-1\\ 5&2&-3\\ 5&6&-3\end{vmatrix}=0$
and $\therefore \, 3 (5x + 2y - 3z) = 6$
$i.e., \, 15 x + 6 y - 9 z = 6 $
Also, $15x + 6 y - 9 z = 5$ and $6 \neq 5$
$\therefore $ the system has no solution.