Consider, the system of equations k x+y+z=1 , x+k y+z=k and x+y+k z=k^ 2 . STATEMENT - 1…
Mathematics · JEE Main · NTA Exams — Matrices and Determinants
Consider, the system of equations \(k x+y+z=1\), \(x+k y+z=k\) and
\(x+y+k z=k^{2}\).
STATEMENT - 1 : System of equations has infinite solutions when \(\mathbf{k}=1\).
STATEMENT - 2 : If the determinant \[\left|\begin{array}{lll} 1 & 1 & 1 \\ k & k & 1 \\ k^{2} & 1 & k \end{array}\right|=0 .\] then \(\mathbf{k}=-1\)
- Both the statements are true and Statement - 2 is the correct explanation of Statement - 1
- Both the statements are true but 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 - 2 is true
Answer
(C) Statement - 1 is true and Statement - 2 is false
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