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AP EAMCET20228 Jul 2022Evening ShiftMathematicsMatricesActual

The rank of the matrix A= [ array cccc 1 & -1 & 0 & -2 -4 & 4 & 0 & 8 -2 & 1 & 2 & 4 array ] is

Options

  1. A1
  2. B0
  3. C3
  4. D2

Correct answer

D. 2

Step-by-step solution

Given, A= [ array cccc 1 & -1 & 0 & -2 -4 & 4 & 0 & 8 -2 & 1 & 2 & 4 array ] Now, we apply elementary transformations, Applying R₃ R₃+2 R₁ and R₂ R₂+4 R₁ , A= [ array cccc 1 & -1 & 0 & -2 0 & 0 & 0 & 0 0 & -1 & 2 & 0 array ] Applying R₂ R₃A= [ array cccc 1 & -1 & 0 & -2 0 & -1 & 2 & 0 0 & 0 & 0 & 0 array ] Matrix A is in row echelon form. Number of non-zero rows =2 Hence, rank of matrix A=2

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