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COMEDK · Maths · 21. Matrices

If the matrix \(A\) is such that \(A\left(\begin{array}{cc}-1 & 2 \\ 3 & 1\end{array}\right)=\left(\begin{array}{cc}-4 & 1 \\ 7 & 7\end{array}\right)\) then \(A\) is equal to

  1. A \(\left(\begin{array}{cc}1 & -1 \\ 2 & 3\end{array}\right)\)
  2. B \(\left(\begin{array}{cc}1 & 1 \\ 2 & -3\end{array}\right)\)
  3. C \(\left(\begin{array}{cc}-1 & 1 \\ 2 & 3\end{array}\right)\)
  4. D \(\left(\begin{array}{cc}1 & 1 \\ -2 & 3\end{array}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\left(\begin{array}{cc}1 & -1 \\ 2 & 3\end{array}\right)\)

Step-by-step Solution

Detailed explanation

Let \(A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}\) and \(B = \begin{pmatrix} -1 & 2 \\ 3 & 1 \end{pmatrix}\). The given equation is \(AB = C\), where \(C = \begin{pmatrix} -4 & 1 \\ 7 & 7 \end{pmatrix}\). To find \(A\), we compute \(A = CB^{-1}\). First, find the…