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Question
State whether the matrix
\[\begin{bmatrix}2 & 3 \\ 6 & 4\end{bmatrix}\] is singular or non-singular.
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Solution
\[\text{ Let }\Delta = \begin{vmatrix} 2 & 3 \\6 & 4 \end{vmatrix} = \left\{ \left( 2 \times 4 \right) - \left( 6 \times 3 \right) \right\} = 8 - 18 = - 10\]
A matrix is said to be singular if its determinant is equal to zero .
\[\text{ Since }\Delta = - 10 \neq 0,\text{ the given matrix is non - singular }.\]
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