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  4. The system of linear equations ax + by = 0, cx + dy = 0 has a non-trivial solution if

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Q. The system of linear equations $ax + by = 0, cx + dy = 0$ has a non-trivial solution if

Matrices

Solution:

System of given equations has a non-trivial
solution if $\begin{vmatrix}a&b\\ c&d\end{vmatrix}$ = 0 $i.e.,$ if $ad - bc$ = 0