Given below are two statements. STATEMENT - 1: If b c+q r=c a+r p=a b+p q=-1 then | array…
Mathematics · JEE Main · NTA Exams — Matrices and Determinants
STATEMENT - 1: If \(b c+q r=c a+r p=a b+p q=-1\) then \[\left|\begin{array}{ccc} a p & a & p \\ b q & b & q \\ c r & c & r \end{array}\right|=0\] \((\mathrm{abc}, \mathrm{pqr} \neq 0)\)
STATEMENT - 2: If system of equations \(a_{1} x+b_{1} y+c_{1}=0_{1} a_{2} x+b_{2} y+c_{2}=0\)\(a_{3} x+b_{3} y+c_{3}=0\) has non-trivial solutions, then \(\left|\begin{array}{lll} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{array}\right|=0\)
In the light of the above statements, choose the correct answer from the options given below:
- Both the statements are true and Statement - 2 is the correct explanation of Statement - 1
- Both the statements are true and Statement - 2 is not the correct explanation of Statement - 1
- Statement - 1 is true and Statement - 2 is false
- Statement - 1 is false and Statement - 1 is true
Answer
(A) Both the statements are true and Statement - 2 is the correct explanation of Statement - 1
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