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AP EAMCET20227 Jul 2022Evening ShiftMathematicsMatricesActual

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

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

C. 2

Step-by-step solution

Convert matrix into row echelon form. aligned & [ array lll 2 & 1 & 2 1 & 0 & 1 4 & 1 & 4 array ] R₁ R₁-R₂ [ array lll 1 & 1 & 1 1 & 0 & 1 4 & 1 & 4 array ] & [ array lll 1 & 1 & 1 1 & 0 & 1 4 & 1 & 4 array ] R₃ R₃-4 R₁ R₂ R₂-R₁ [ array ccc 1 & 1 & 1 0 & -1 & 0 0 & -3 & 0 array ] & [ array lll 1 & 1 & 1 0 & -1 & 0 0 & -3 & 0 array ] [R₃ (- 1 3 ) R₃] R₂ (-1) R₂ [ array lll 1 & 1 & 1 0 & 1 & 0 0 & 3 & 0 array ] & [ array lll 1 & 1 & 1 0 & 1 & 0 0 & 3 & 0 array ] R₃ R₃-R₂ [ array lll 1 & 1 & 1 0 & 1 & 0 0 & 0 & 0 arra

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