The value of the determinant left| begin{arra | vedclass

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(C) Let $\Delta = \left| \begin{array}{ccc} 1 & 2 & 3 \ 3 & 5 & 7 \ 8 & 14 & 20 \end{array} ight|$.Applying the column operation $C_3 	o C_3 - C_

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$0$

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(C) Let $\Delta = \left| \begin{array}{ccc} 1 & 2 & 3 \ 3 & 5 & 7 \ 8 & 14 & 20 \end{array} ight|$.Applying the column operation $C_3 	o C_3 - C_2$:$\Delta = \left| \begin{array}{ccc} 1 & 2 & 1 \ 3 & 5 & 2 \ 8 & 14 & 6 \end{array} ight|$.Applying the column operation $C_2 	o C_2 - 2C_1$:$\Delta = \left| \begin{array}{ccc} 1 & 0 & 1 \ 3 & -1 & 2 \ 8 & -2 & 6 \end{array} ight|$.Expanding along the first row:$\Delta = 1((-1)(6) - (2)(-2)) - 0 + 1((3)(-2) - (-1)(8))$$\Delta = 1(-6 + 4) + 1(-6 + 8)$$\Delta = 1(-2) + 1(2) = -2 + 2 = 0$.Thus,the value of the determinant is $0$.

The value of the determinant $\left| \begin{array}{ccc} 1 & 2 & 3 \\ 3 & 5 & 7 \\ 8 & 14 & 20 \end{array} \right|$ is

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