Question:
If the product and sum of eigenvalues of a 2 × 2 matrix
\[
\begin{pmatrix}
3 & x \\
x & y
\end{pmatrix}
\]
are -3 and 5, respectively, then \( x + y = \_\_\_ \)
If the product and sum of eigenvalues of a 2 × 2 matrix
\[
\begin{pmatrix}
3 & x \\
x & y
\end{pmatrix}
\]
are -3 and 5, respectively, then \( x + y = \_\_\_ \)
Show Hint
To solve for the sum and product of eigenvalues, use the trace and determinant of the matrix.
Updated On: Jun 16, 2025
- -5
- -6 $\pm$ i$\sqrt{3}$
- -2 $\pm$ i3
- -1
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The Correct Option is D
Solution and Explanation
The sum and product of eigenvalues are the trace and determinant of the matrix, respectively.
For the given matrix, the trace is $3 + y$ and the determinant is $3y - x^2$.
Using the given sum and product of eigenvalues, we can solve for $x + y = -1$.
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