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AP EAMCET · Maths · Determinants

\(\left|\begin{array}{ccc}
a+b+2 c & a & b \\
c & b+c+2 a & b \\
c & a & c+a+2 b
\end{array}\right|=\)

  1. A \((a+b+c)^3\)
  2. B \(2(a+b+c)^3\)
  3. C \(3(a+b+c)^3\)
  4. D \((a+b+c)\)
Verified Solution

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 \(\Rightarrow \Delta=2(a+b+c)\left|\begin{array}{ccc} 1 & a & b \\ 1 & 2 a+b+c & b \\ 1 & a & a+2 b+c \end{array}\right|\)…