AP EAMCET · Maths · Determinants
The equation obtained by eliminating \(a, b, c\) from the equations \(x=\frac{a}{b-c}, y=\frac{b}{c-a}\), \(z=\frac{c}{a-b}\) is
- A \(\left|\begin{array}{lll}1 & -x & x \\ 1 & -y & y \\ 1 & -z & z\end{array}\right|=0\)
- B \(\left|\begin{array}{ccc}1 & -x & x \\ 1 & 1 & -y \\ 1 & z & 1\end{array}\right|=0\)
- C \(\left|\begin{array}{ccc}1 & -x & x \\ y & 1 & -y \\ -z & z & -1\end{array}\right|=0\)
- D \(\left|\begin{array}{lll}x & y & 1 \\ y & x & 1 \\ 1 & x & y\end{array}\right|=0\)
Answer & Solution
Correct Answer
(B) \(\left|\begin{array}{ccc}1 & -x & x \\ 1 & 1 & -y \\ 1 & z & 1\end{array}\right|=0\)
Step-by-step Solution
Detailed explanation
Given equations \(\begin{gathered} x=\frac{a}{b-c} \Rightarrow a-b x+c x=0 \\ y=\frac{b}{c-a} \Rightarrow a y+b-c y=0 \end{gathered}\) and \(\quad z=\frac{c}{a-b} \Rightarrow a z-b z-c=0\) Now, on eliminating \(a, b, c\) from the above equations, we get…
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