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AP EAMCET · Maths · Matrices

A value of \(b\) for which the rank of the matrix \(A=\left[\begin{array}{cccc}1 & 1 & -1 & 0 \\ 4 & 4 & -3 & 1 \\ b & 2 & 2 & 2 \\ 9 & 9 & b & 3\end{array}\right]\) is 3 , is

  1. A -2
  2. B -4
  3. C -6
  4. D 3
Verified Solution

Answer & Solution

Correct Answer

(C) -6

Step-by-step Solution

Detailed explanation

Given, \[ A=\left[\begin{array}{cccc} 1 & 1 & -1 & 0 \\ 4 & 4 & -3 & 1 \\ b & 2 & 2 & 2 \\ 9 & 9 & b & 3 \end{array}\right] \] For rank to be 3, there must exist 3 non zero row. Now, applying \(R_2 \rightarrow R_2-4 R_1 ; R_3 \rightarrow R_3-2 R_1\)…