Q46 / 160 · AP EAMCET 2024 (23 May Shift 1) · Mathematics

If the system of equations $a_1 x+b_1 y+c_1 z=0$, $a_2 x+b_2 y+c_2 z=0, \quad a_3 x+b_3 y+c_3 z=0$ has only trivial solution, then the rank of $\left[\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right]$ is

  • A
    2
  • B
    1
  • Correct answer
    C
    3
  • D
    0

Solution

If the system of equations $a_1 x+b_1 y+c_1=0$, $a_2 x+b_2 y+c_2 z=0$, and $a_3 x+b_3 y+c_3=0$ has only trivial solution, then rank of the matrix $\left[\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right]$ is 3 .

Hence, the correct answer is option: 'C'.

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