Which of the following matrices are singular or non-singular? [ c… - Vidyadip

Question

Which of the following matrices are singular or non-singular?

$\left[\begin{array}{ccc}3 & 5 & 7 \\ -2 & 1 & 4 \\ 3 & 2 & 5\end{array}\right]$

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Answer

Let $A=\left[\begin{array}{ccc}3 & 5 & 7 \\ -2 & 1 & 4 \\ 3 & 2 & 5\end{array}\right]$

$\therefore|A|=\left|\begin{array}{ccc}3 & 5 & 7 \\ -2 & 1 & 4 \\ 3 & 2 & 5\end{array}\right|$

= 3(5 – 8) – 5(-10 – 12) + 7(-4 – 3) = -9 + 110 – 49 = 52 ≠ 0 ∴ A is a non-singular matrix.

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