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Consider the following matrix $$A = \left[\begin{array}{cc}2 & 3\\x & y \end{array}\right]$$ If the eigenvalues of A are 4 and 8, then

1. x = 4, y = 10
2. x = 5, y = 8
3. x = 3,y = 9
4. x = -4, y = 10
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Sum of eighen values is equal to trace(sum of diagonal elements),and product of eighen values is equal to det of matrix

So 2+y=8+4

y =10

2y-3x = 32

Solving this we get

x =-4

Option d is ans
edited
Solve the equation 3x 2y=8 and x 2y=16 which i get x= -4 ,y = 10
using one simple property...

The sum of eigen values is equal to the sum of the diagonal elements.

Given that the eigen values are 4 and 8, we have,

8+4 = y + 2

y = 10.

Now out of A and D, I don't find any difference in the options.