ExamBro
ExamBro
MHT CET · Maths · Determinants

If \(A=\left[\begin{array}{ccc}5 & 6 & 3 \\ -4 & 3 & 2 \\ -4 & -7 & 3\end{array}\right]\), then cofactors of all elements of second row are respectively.

  1. A \(-39,3,11\)
  2. B \(-39,27,11\)
  3. C \(39,-3-11\)
  4. D \(-39,-27,11\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(-39,27,11\)

Step-by-step Solution

Detailed explanation

\(
A=\left[\begin{array}{ccc}
5 & 6 & 3 \\
-4 & 3 & 2 \\
-4 & -7 & 3
\end{array}\right]
\)
Cofactors of elements in second row are
Cofactor of -4
Cofactor of 3
\(
\begin{aligned}
& =(-1)^{2+1}\left|\begin{array}{cc}
6 & 3 \\
-7 & 3
\end{array}\right|=-(18+21)=-39 \\
& =(-1)^{2+2}\left|\begin{array}{cc}
5 & 3 \\
-4 & 3
\end{array}\right|=15+12=27 \\
& =(-1)^{2+3}\left|\begin{array}{cc}
5 & 6 \\
-4 & -7
\end{array}\right|=-(-35+24)=11
\end{aligned}
\)