JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A=\left[\begin{array}{lll}x & y & z \\ y & z & x \\ z & x & y\end{array}\right], \quad\) where \(x, y\) and \(z\) are real numbers such that \(x + y + z >0\) and \(xyz =2\) If \(A ^{2}= I _{3},\) then the value of \(x ^{3}+ y ^{3}+ z ^{3}\) is ............
- A \(7\)
- B \(5\)
- C \(9\)
- D \(6\)
Answer & Solution
Correct Answer
(A) \(7\)
Step-by-step Solution
Detailed explanation
\(A ^{2}= I\) \(\left(\right.\) as \(\left.A^{\prime}=A\right)\) \(\Rightarrow AA ^{\prime}= I\) \(\Rightarrow A\) is orthogonal So, \(x^{2}+y^{2}+z^{2}=1\) and \(x y+y z+z x=0\) \(\Rightarrow(x+y+z)^{2}=1+2 \times 0\) \(\Rightarrow x+y+z=1\) Thus,…
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