JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(x, y, z\) are in arithmetic progression with common difference \(d , x \neq 3 d ,\) and the
determinant of the matrix \(\left[\begin{array}{ccc}3 & 4 \sqrt{2} & x \\ 4 & 5 \sqrt{2} & y \\ 5 & k & z\end{array}\right]\) is zero, then the value of \(k ^{2}\) is ..... .
- A \(72\)
- B \(12\)
- C \(36\)
- D \(6\)
Answer & Solution
Correct Answer
(A) \(72\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{ccc}3 & 4 \sqrt{2} & x \\ 4 & 5 \sqrt{2} & y \\ 5 & k & z\end{array}\right|=0\) \(R _{2} \rightarrow R _{1}+ R _{3}-2 R _{2}\) \(\Rightarrow\left|\begin{array}{ccc}3 & 4 \sqrt{2} & x \\ 0 & k-6 \sqrt{2} & 0 \\ 5 & k & z\end{array}\right|=0\)…
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