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MHT CET202015 Oct 2020Evening ShiftMathematicsMatricesActual

If A= [ array cc 1 & 0 -1 & 7 array ], I= [ array cc 1 & 0 0 & 1 array ] and A²=8 A+k I , then the value of K is

Options

  1. A1 7
  2. B-1 7
  3. C-7
  4. D7

Correct answer

C. -7

Step-by-step solution

A²=A A= [ array cc 1 & 0 -1 & 7 array ] [ array cc 1 & 0 -1 & 7 array ]= [ array cc 1 & 0 -8 & 49 array ] Given A²=8 A+K I aligned &=8 [ array cc 1 & 0 -1 & 7 array ]+ k [ array ll 1 & 0 0 & 1 array ]= [ array cc 8 & 0 -8 & 56 array ]+ [ array cc k & 0 0 & k array ] [ array cc 1 & 0 -8 & 49 array ] &= [ array cc 8+ k & 0 -8 & 56+ k array ] 8+ k =1 k =-7 aligned

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