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AP EAMCET · Maths · Matrices

Which of the following matrix has rank 3?

  1. A \(\left[\begin{array}{ccc}10 & 11 & 12 \\ 11 & 12 & 13 \\ 12 & 13 & 14\end{array}\right]\)
  2. B \(\left[\begin{array}{ccc}0 & -51 & 101 \\ 51 & 0 & -581 \\ -101 & 581 & 0\end{array}\right]\)
  3. C \(\left[\begin{array}{ccc}0 & 1 & 2 \\ -1 & 0 & 5 \\ -2 & 7 & 0\end{array}\right]\)
  4. D \(\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9\end{array}\right]\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\left[\begin{array}{ccc}0 & 1 & 2 \\ -1 & 0 & 5 \\ -2 & 7 & 0\end{array}\right]\)

Step-by-step Solution

Detailed explanation

Option (a) Let \(A=\left[\begin{array}{lll}10 & 11 & 12 \\ 11 & 12 & 13 \\ 12 & 13 & 14\end{array}\right]\) Applying \(R_1 \rightarrow R_1-R_2, R_2 \rightarrow R_2-R_3\) \[ \left[\begin{array}{ccc} -1 & -1 & -1 \\ -1 & -1 & -1 \\ 12 & 13 & 14 \end{array}\right] \] Applying…