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COMEDK2017MathematicsMatrices

If A= [ array cc 2 & -3 5 & -7 array ] , then A+A⁻¹=

Options

  1. A[ array ll 1 & 0 0 & 1 array ]
  2. B[ array cc -5 & 0 0 & -5 array ]
  3. C[ array ll 5 & 0 0 & 5 array ]
  4. D[ array cc 4 & 0 0 & -5 array ]

Correct answer

B. [ array cc -5 & 0 0 & -5 array ]

Step-by-step solution

A= [ array cc 2 & -3 5 & -7 array ] |A|=-14+15=1 0 So, A⁻¹ exists. aligned & adj A= [ array ll -7 & 3 -5 & 2 array ] & A⁻¹= 1 |A| ( adj A)= [ array cc -7 & 3 -5 & 2 array ] aligned aligned A+A⁻¹ &= [ array cc 2 & -3 5 & -7 array ]+ [ array ll -7 & 3 -5 & 2 array ] &= [ array cc -5 & 0 0 & -5 array ] aligned

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