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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. A4 [ array ll 2 & 1 2 & 0 array ]
  2. B4 [ array cc 0 & -1 2 & 2 array ]
  3. C32 [ array ll 2 & 1 2 & 0 array ]
  4. D32 [ 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 ll 8 & 4 8 & 0 array ] & =4 [ array ll 2 & 1 2 & 0 array ] aligned

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