Evaluate the determinant: left| begin{array}{ | vedclass

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(A) Given the determinant $\Delta = \left| \begin{array}{ccc} a_1 & m a_1 & b_1 \ a_2 & m a_2 & b_2 \ a_3 & m a_3 & b_3 \end{array} ight|$.By taki

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$0$

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(A) Given the determinant $\Delta = \left| \begin{array}{ccc} a_1 & m a_1 & b_1 \ a_2 & m a_2 & b_2 \ a_3 & m a_3 & b_3 \end{array} ight|$.By taking the common factor $m$ from the second column $(C_2)$,we get:$\Delta = m \left| \begin{array}{ccc} a_1 & a_1 & b_1 \ a_2 & a_2 & b_2 \ a_3 & a_3 & b_3 \end{array} ight|$.Since the first column $(C_1)$ and the second column $(C_2)$ are identical $(C_1 = C_2)$,the value of the determinant is $0$.Therefore,$\Delta = m 	imes 0 = 0$.

Evaluate the determinant: $\left| \begin{array}{ccc} a_1 & m a_1 & b_1 \\ a_2 & m a_2 & b_2 \\ a_3 & m a_3 & b_3 \end{array} \right|$

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