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KCET2012MathematicsMatrices

The characteristic equation of a matrix A is ³-5 ²-3 +2=0 , then adj (A) is equal to

Options

  1. A9
  2. B25
  3. C1 2
  4. D4

Correct answer

D. 4

Step-by-step solution

We know that, [ array ccc 0 & 0 & - c 1 & 0 & - b 0 & 1 & - a array ] iff ³+ a ²+ b + c =0 But given that, ³-5 ²-3 +2=0A= [ array rrr 0 & 0 & -2 1 & 0 & 3 0 & 1 & 5 array ]|A|= [ array rrr 0 & 0 & -2 1 & 0 & 3 0 & 1 & 5 array ]=0+0-2(1-0)=-2 adj . A |=| A |²=(-2)²=4

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