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State Whether the Matrix [ 2 3 6 4 ] is Singular Or Non-singular. - Mathematics

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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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Chapter 6: Determinants - Exercise 6.6 [Page 90]

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RD Sharma Mathematics [English] Class 12
Chapter 6 Determinants
Exercise 6.6 | Q 4 | Page 90

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