JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
For the system of linear equations \(a x+y+z=1\), \(x+a y+z=1, x+y+a z=\beta\), which one of the following statements is NOT correct ?
- A It has infinitely many solutions if \(\alpha=2\) and \(\beta=-1\)
- B It has no solution if \(\alpha=-2\) and \(\beta=1\)
- C \(x+y+z=\frac{3}{4}\) if \(\alpha=2\) and \(\beta=1\)
- D It has infinitely many solutions if \(\alpha=1\) and \(\beta=1\)
Answer & Solution
Correct Answer
(A) It has infinitely many solutions if \(\alpha=2\) and \(\beta=-1\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{lll}\alpha & 1 & 1 \\ 1 & \alpha & 1 \\ 1 & 1 & \alpha\end{array}\right|=0\) \(\alpha\left(\alpha^2-1\right)-1(\alpha-1)+1(1-\alpha)=0\) \(\alpha^3-3 \alpha+2=0\) \(\alpha^2(\alpha-1)+\alpha(\alpha-1)-2(\alpha-1)=0\)…
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