The lines 2x + y - 1 = 0,ax + 3y - 3 = 0,and | vedclass

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(A) Three lines $a_1x + b_1y + c_1 = 0$,$a_2x + b_2y + c_2 = 0$,and $a_3x + b_3y + c_3 = 0$ are concurrent if the determinant of their coefficients is

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(A) Three lines $a_1x + b_1y + c_1 = 0$,$a_2x + b_2y + c_2 = 0$,and $a_3x + b_3y + c_3 = 0$ are concurrent if the determinant of their coefficients is zero:$\begin{vmatrix} 2 & 1 & -1 \ a & 3 & -3 \ 3 & 2 & -2 \end{vmatrix} = 0$Expanding the determinant along the first row:$2(3(-2) - (-3)(2)) - 1(a(-2) - (-3)(3)) - 1(a(2) - 3(3)) = 0$$2(-6 + 6) - 1(-2a + 9) - 1(2a - 9) = 0$$2(0) + 2a - 9 - 2a + 9 = 0$$0 = 0$Since the determinant is zero regardless of the value of $a$,the lines are concurrent for all values of $a$.

The lines $2x + y - 1 = 0$,$ax + 3y - 3 = 0$,and $3x + 2y - 2 = 0$ are concurrent for

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