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TS EAMCET · Maths · Determinants

Match the following elements of \(\left[\begin{array}{ccc}1 & -1 & 0 \\ 0 & 4 & 2 \\ 3 & -4 & 6\end{array}\right]\) with their co-factors and choose the correct answer.
\(\begin{array}{lcll} & \text { Element } & & \text { Co-factor } \\ \text { A. } & -1 & \text { (1) } & -2 \\ \text { B. } & 1 & (2) & 32 \\ \text { C. } & 3 & (3) & 4 \\ \text { D. } & 6 & \text { (4) } & 6 \\ & & \text { (5) } & -6\end{array}\)

  1. A \(\begin{array}{llll}\text { A } & \text { B } & \text { C } & \text { D } \\ 2 & 4 & 1 & 3\end{array}\)
  2. B \(\begin{array}{llll}\text { A } & \text { B } & \text { C } & \text { D } \\ 2 & 4 & 3 & 1\end{array}\)
  3. C \(\begin{array}{llll}\text { A } & \text { B } & \text { C } & \text { D } \\ 4 & 2 & 1 & 3\end{array}\)
  4. D \(\begin{array}{llll}\text { A } & \text { B } & \text { C } & \text { D } \\ 4 & 1 & 2 & 3\end{array}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\begin{array}{llll}\text { A } & \text { B } & \text { C } & \text { D } \\ 4 & 2 & 1 & 3\end{array}\)

Step-by-step Solution

Detailed explanation

Let \(A=\left[\begin{array}{ccc}1 & -1 & 0 \\ 0 & 4 & 2 \\ 3 & -4 & 6\end{array}\right]\) Cofactor of \((-1)=-\left|\begin{array}{ll}0 & 2 \\ 3 & 6\end{array}\right|=6\) Cofactor of \((1)=\left|\begin{array}{cc}4 & 2 \\ -4 & 6\end{array}\right|=24+8=32\) Cofactor of…