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AP EAMCET · Maths · Matrices

Consider the matrices
\(A=\left[\begin{array}{ccc}
x & y & 0 \\
-3 & 1 & 2 \\
1 & -2 & z
\end{array}\right] \text { and } B=\left[\begin{array}{ccc}
1 & -2 & -2 \\
2 & 0 & 1 \\
2 & 1 & 0
\end{array}\right]\)
If the cofactors of the elements \(z, 1\) in \(3{ }^{\text {rd }}\) row and \(x\) of \(A\) are \(9,4,3\) respectively then \(A B=\)

  1. A \(\left[\begin{array}{ccc}-7 & -4 & -8 \\ -1 & 8 & 7 \\ 3 & -3 & -4\end{array}\right]\)
  2. B \(\left[\begin{array}{ccc}7 & -6 & 8 \\ -5 & 4 & -5 \\ -5 & -3 & -4\end{array}\right]\)
  3. C \(\left[\begin{array}{ccc}7 & -6 & -4 \\ 3 & 8 & 7 \\ -5 & -3 & -4\end{array}\right]\)
  4. D \(\left[\begin{array}{ccc}7 & -6 & 8 \\ -1 & 8 & -5 \\ 3 & -3 & -4\end{array}\right]\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\left[\begin{array}{ccc}7 & -6 & -4 \\ 3 & 8 & 7 \\ -5 & -3 & -4\end{array}\right]\)

Step-by-step Solution

Detailed explanation

\(C_{31} = 2y = 4 \implies y = 2\) \(C_{11} = z+4 = 3 \implies z = -1\) \(C_{33} = x+3y = 9 \implies x+3(2) = 9 \implies x = 3\) \(A=\left[\begin{array}{ccc}3 & 2 & 0 \\ -3 & 1 & 2 \\ 1 & -2 & -1\end{array}\right]\)…