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AP EAMCET2014MathematicsMatrices

If the matrix A= [ array cccc 1 & 2 & 3 & 0 2 & 4 & 3 & 2 3 & 2 & 1 & 3 6 & 8 & 7 & array ] is of rank 3, then equals to

Options

  1. A-5
  2. B5
  3. C4
  4. D1

Correct answer

B. 5

Step-by-step solution

Given, A= [ array cccc 1 & 2 & 3 & 0 2 & 4 & 3 & 2 3 & 2 & 1 & 3 6 & 8 & 7 & array ] Applying R₂ R₂-2 R₁, R₃ R₃-3 R₁ and aligned R₄ R₄ & -2 R₃ = & [ array rrrr 1 & 2 & 3 & 0 0 & 0 & -3 & 2 0 & -4 & -8 & 3 0 & 4 & 5 & -6 array ] aligned Applying R₄ R₄+R₃ = [ array rrrr 1 & 2 & 3 & 0 0 & 0 & -3 & 2 0 & -4 & -8 & 3 0 & 0 & -3 & -3 array ] Applying R₄ R₄-R₂ = [ array rrrr 1 & 2 & 3 & 0 0 & 0 & -3 & 2 0 & -4 & -8 & 3 0 & 0 & 0 & -5 array ] Since, the matrix A is of rank 3 . -5=0 =5

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