Mathematics

Mathematics

Problem

If a1x+b1y+c1z=0,  a2x+b2y+c2z=0,a_1 x + b_1 y + c_1 z = 0,\; a_2 x + b_2 y + c_2 z = 0, a3x+b3y+c3z=0 and ∣a1b1c1a2b2c2a3b3c3∣=0, then given system hasa_3 x + b_3 y + c_3 z = 0 \text{ and } \begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix} = 0, \text{ then given system has} (a) One trivial and one non-trivial solution (b) No solution (c) One solution (d) Infinite solution (a) One trivial and one non-trivial solution (b) No solution (c) One solution (d) Infinite solution

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