TS EAMCET · Maths · Determinants
\(\left|\begin{array}{ccc}a-b-c & 2 a & 2 a \\ 2 b & b-c-a & 2 b \\ 2 c & 2 c & c-a-b\end{array}\right|\) is equal to
- A \(0\)
- B \(a+b+c\)
- C \((a+b+c)^2\)
- D \((a+b+c)^3\)
Answer & Solution
Correct Answer
(D) \((a+b+c)^3\)
Step-by-step Solution
Detailed explanation
Let \(\Delta=\left[\begin{array}{ccc}a-b-c & 2 a & 2 a \\ 2 b & b-c-a & 2 b \\ 2 c & 2 c & c-a-b\end{array}\right]\) Applying \(\quad R_1 \rightarrow R_1+R_2+R_3 \quad\) and taking common \((a+b+c)\) from \(R_1\)…
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