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The eigen values of the following matrix are 
  • a)
    3, 3 + 5j, –6 – j    
  • b)
    –6 + 5j, 3 + j, 3 – j 
  • c)
    3+ j, 3 – j, 5 + j    
  • d)
    3, –1 + 3j, –1 – 3j 
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The eigen values of the following matrix area)3, 3 + 5j, –6 R...
Let the matrix be A.  We know, Trace (A)=sum of eigen values. 
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The eigen values of the following matrix area)3, 3 + 5j, –6 R...
Sum of the eigen values = trace of the matrix Trace = 3-1-1= 1 In option d only, the summation of the eigen values is equal to 1.i.e. [ 3 - 1 + 3j - 1 - 3j = 1]
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Community Answer
The eigen values of the following matrix area)3, 3 + 5j, –6 R...
since last row has only one element then we can directly write 3 - λ = 0. now one of the Eigen value is 3. thus option narrows down to a , d. now the sum of Eigen values is trace of matrix. trace is 1 ( sum of principal diagonal elements.) now from option d) 3 + -1 + 3j + -1 + -1 + -3j = 1 since (+3j + -3j = 0 ) .
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The eigen values of the following matrix area)3, 3 + 5j, –6 – j b)–6 + 5j, 3 + j, 3 – jc)3+ j, 3 – j, 5 + j d)3, –1 + 3j, –1 – 3jCorrect answer is option 'D'. Can you explain this answer?
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