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Let A be a  matrix with eigen values -5,-2,1,4. Which of the following is an eigen value of  the matrix , where   identity matrix?  
  • a)
    -5
  • b)
    -7
  • c)
    2
  • d)
    1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let A be a matrix with eigen values -5,-2,1,4. Which of the following ...

So, for our given matrix, we have

This is a
 block matrix where the first and last and the second and third elements are the same. So, applying the formulafor determinant of a block matrix as given here (second last case)

Each of the eigen value of A is the solution of the equation  . So, we can equate   to any of the eigen value of A, and that will get our value of  and that is one of the choice. For no other choice, this equation holds. So, (c) 2 is the answer.
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Let A be a matrix with eigen values -5,-2,1,4. Which of the following is an eigen value of the matrix, where identity matrix? a)-5b)-7c)2d)1Correct answer is option 'C'. Can you explain this answer?
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