AP EAMCET · Maths · Determinants
\(\left|\begin{array}{ccc}
a+b+2 c & a & b \\
c & b+c+2 a & b \\
c & a & c+a+2 b
\end{array}\right|=\)
- A \((a+b+c)^3\)
- B \(2(a+b+c)^3\)
- C \(3(a+b+c)^3\)
- D \((a+b+c)\)
Answer & Solution
Correct Answer
(B) \(2(a+b+c)^3\)
Step-by-step Solution
Detailed explanation
\(\Delta=\left|\begin{array}{ccc}a+b+2 c & a & b \\ c & b+c+2 a & b \\ c & a & c+a+2 b\end{array}\right|\) Applying, \(C_1 \rightarrow C_1+C_2+C_3\), we get \(\Rightarrow \Delta=2(a+b+c)\left|\begin{array}{ccc} 1 & a & b \\ 1 & 2 a+b+c & b \\ 1 & a & a+2 b+c \end{array}\right|\)…
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