Consider the system of equations a 1 x + b 1 y + c 1 z = 0, a 2 x + b 2 y + c 2 z = 0, a…
Mathematics · JEE Main · NTA Exams — Matrices and Determinants
Consider the system of equations a1x + b1y + c1z = 0, a2x + b2y + c2z = 0, a3x + b3y + c3z = 0 if
\[\left|\begin{array}{lll} \mathrm{a}_{1} & \mathrm{~b}_{1} & \mathrm{c}_{1} \\ \mathrm{a}_{2} & \mathrm{~b}_{2} & \mathrm{c}_{2} \\ \mathrm{a}_{3} & \mathrm{~b}_{3} & \mathrm{c}_{3} \end{array}\right|\] = 0, then the system has
\[\left|\begin{array}{lll} \mathrm{a}_{1} & \mathrm{~b}_{1} & \mathrm{c}_{1} \\ \mathrm{a}_{2} & \mathrm{~b}_{2} & \mathrm{c}_{2} \\ \mathrm{a}_{3} & \mathrm{~b}_{3} & \mathrm{c}_{3} \end{array}\right|\] = 0, then the system has
- more than two solutions
- only non trivial solutions
- no solution
- only trivial solution (0, 0,0).
Answer
(A) more than two solutions
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