AP EAMCET · Maths · Matrices
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
- C 3
- D 0
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
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 .
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