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KCET2010MathematicsMatrices

If A= [ array ll 3 & 2 1 & 1 array ] , then A²+x A+y I=0 for (x, y) is

Options

  1. A(-4,1)
  2. B(-1,3)
  3. C(4,-1)
  4. D(1,3)

Correct answer

A. (-4,1)

Step-by-step solution

A= [ array ll 3 & 2 1 & 1 array ] The characteristic equation of ' A ' is array r | A - I |=0 | array cc 3- & 2 1 & 1- array |=0 (3- )(1- )-2=0 3- -3 + ²-2=0 ( ²-4 +1 )=0 ...(i) array By Caylay-Hamilton theorem : Every square matrix satisfied its characteristic equation, then put ( = A ) is in Eq. (i) aligned & A ²-4 ~A + I =0 & On comparing with A ²+ xA + yI =0 & x =-4, y =1 aligned

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