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GUJCET · Maths · Determinants
If \(x^4+y^4+z^4=0\) then, \(\left|\begin{array}{ccc}1 & x y & y z \\ z x & 1 & x y \\ y z & z x & 1\end{array}\right|=\) ____________ . \((\because x, y, z \in R )\)
- A 1
- B \(x+y+z+3\)
- C \(x y z+2\)
- D 0
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
Given \(x^4+y^4+z^4=0\) for \(x, y, z \in R\), then \(x=0, y=0, z=0\). \(\left|\begin{array}{ccc}1 & x y & y z \\ z x & 1 & x y \\ y z & z x & 1\end{array}\right| = \left|\begin{array}{ccc}1 & 0 \cdot 0 & 0 \cdot 0 \\ 0 \cdot 0 & 1 & 0 \cdot 0 \\ 0 \cdot 0 & 0 \cdot 0 & 1\end{array}\right|\)
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