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  be a matrix with real entries. If the sum and the product of all the eigenvalues
of A are 10 30 respectively, then a2 + b2 equals
  • a)
    29
  • b)
    40
  • c)
    58
  • d)
    65
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
be a matrix with real entries. If the sum and the product of all the e...
It's an upper triangular matrix. So its eigen values are nothing, but the diagonal elements,which are a, b & 3.
Hence, a+b+3=10
=> a+b = 7
Again, a×b×3 = 30
=> a×b = 10
So we know the identity :
a²+b²=(a+b)² - 2ab
= 49 - 20 = 29
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Community Answer
be a matrix with real entries. If the sum and the product of all the e...
29
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