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### Answers (1)

Answer:$\left|\begin{array}{ccc} 8 & 2 & 7 \\ 12 & 3 & 5 \\ 16 & 4 & 3 \end{array}\right|=0$

Hint: We will try to do any two column or row equal

Given:$\left|\begin{array}{ccc} 8 & 2 & 7 \\ 12 & 3 & 5 \\ 16 & 4 & 3 \end{array}\right|$

Solution:$\left|\begin{array}{ccc} 8 & 2 & 7 \\ 12 & 3 & 5 \\ 16 & 4 & 3 \end{array}\right|$

\begin{aligned} &\text { On taking common } 4 \text { from } \mathrm{C}_{1}\\ &=4\left|\begin{array}{lll} 2 & 2 & 7 \\ 3 & 3 & 5 \\ 4 & 4 & 3 \end{array}\right| \end{aligned}

If any two rows or columns of a determinant are identical.

The value of the determinant is zero

\begin{aligned} &=4 \times 0 \quad\left(\because C_{1}=C_{2}\right) \\ &=0 \end{aligned}

Hence $\left|\begin{array}{ccc} 8 & 2 & 7 \\ 12 & 3 & 5 \\ 16 & 4 & 3 \end{array}\right|=0$

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