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
2y-3x=32
x=-4 , b= 10
Similar question: GATE CSE 2015 Set 1 | Question: 36
As we know The product of eigenvalue is equal to Determinant. So in this question, eigenvalues are given 4 and 8. So are determinant is 32. Now we can put the value of X and Y and check whether the determinant is equal to 32 or not
I found one more interesting solution, which will give you intuition as per @sachin sir language.
Follow the steps:
I know the solution provided by Pooja is faster but it is also an interesting way to think about the solution.
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