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If 2 and -4 are the eigenvalues of a non-singular matrix A and |A| = -8, then the eigenvalues of adj(A) are x and -y. What is the value of x+y?
in Linear Algebra
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my answer: 6

how i solved:

eigenvalues of adj(A) = |A| / eigenvalues of A = -8/2 and -8/-4 = -4 and 2. hence, x = 2, y = 4. so, x + y = 6.

however, answer key: -6
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X= (-8)/2 = – 4

Y= (-8)/-4 = 2

But Adj of A is given X and -Y so values will be X= -4 and -Y = -2

So total would be -4 -2 = -6 Answer key is correct.
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You have solved it correctly @atulcse , test series often have this type of mistakes so don’t bother about this too much.

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@atulcse

 

A=[2    0

     0  −4] ...

Adj (A)= [−4  0

                0  2 ] ...

Here x=−4 and −y=2

⇒y = −2

⇒x+y  = (−4) − 2 

= −6 …

 

1. https://gateoverflow.in/290887/Made-easy 

 

 

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