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MHT CET · Maths · Matrices

If matrix \(A=\frac{1}{11}\left[\begin{array}{rrr}-1 & 7 & -24 \\ 2 & a & 4 \\ 2 & -3 & 15\end{array}\right]\) and \(A^{-1}=\left[\begin{array}{rrr}3 & 3 & 4 \\ 2 & -3 & 4 \\ b & -1 & c\end{array}\right]\), then the values of \(a, b, c\) respectively are ......

  1. A \(3,1,0\)
  2. B \(\frac{-6}{11}, 0, \frac{1}{11}\)
  3. C \(-3,0,1\)
  4. D \(\frac{-3}{11}, 0, \frac{1}{11}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(-3,0,1\)

Step-by-step Solution

Detailed explanation

\(\frac{1}{11}\left[\begin{array}{rrr}-1 & 7 & -24 \\ 2 & a & 4 \\ 2 & -3 & 15\end{array}\right]\left[\begin{array}{rrr}3 & 3 & 4 \\ 2 & -3 & 4 \\ b & -1 & c\end{array}\right] = \left[\begin{array}{rrr}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]\) \(\left[\begin{array}{rrr}-1 & 7 & -24 \\ 2 & a & 4 \\ 2 & -3 & 15\end{array}\right]\left[\begin{array}{rrr}3 & 3 & 4 \\ 2 & -3 & 4 \\ b & -1 & c\end{array}\right] = \left[\begin{array}{rrr}11 & 0 & 0 \\ 0 & 11 & 0 \\ 0 & 0 & 11\end{array}\right]\)