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BITSAT2011MathematicsMatricesActual

The matrix (A^2+4 A-5 I ), where (I ) is identity matrix and (A= [ array cc 1 & 2 4 & -3 array ] ), equals :

Options

  1. A(4 [ array ll 2 & 1 2 & 0 array ] )
  2. B(4 [ array cc 0 & -1 2 & 2 array ] )
  3. C(32 [ array ll 2 & 1 2 & 0 array ] )
  4. D(32 [ array ll 1 & 1 1 & 0 array ] )

Correct answer

A. (4 [ array ll 2 & 1 2 & 0 array ] )

Step-by-step solution

( aligned & A^2+4 A-5 I=A A+4 A-5 I = & [ array cc 1 & 2 4 & -3 array ] [ array cc 1 & 2 4 & -3 array ]+4 [ array cc 1 & 2 4 & -3 array ]-5 [ array ll 1 & 0 0 & 1 array ] = & [ array cc 9 & -4 -8 & 17 array ]+ [ array cc 4 & 8 16 & -12 array ]- [ array cc 5 & 0 0 & 5 array ] = & [ array cc 9+4-5 & -4+8-0 -8+16-0 & 17-12-5 array ]= [ array cc 8 & 4 8 & 0 array ] = & 4 [ array cc 2 & 1 2 & 0 array ] aligned )

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