Home › Previous year questions › GATE 2010 CS (CS1) › Question 39GATE 2010 CS (CS1) – Question 39 Engineering Mathematics · Linear Algebra · 2 marks · Multiple choice
The matrix $\begin{pmatrix}2&3\\x&y\end{pmatrix}$ has eigenvalues 4 and 8. Find x,y.
x=4,y=10 x=5,y=8 x=−3,y=9 x=−4,y=10 Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (D) x=−4,y=10
Explanation The trace equals the sum of eigenvalues: 2+y=12, giving y=10. The determinant equals their product: 2y−3x=32. Substituting gives 20−3x=32, hence x=−4. Thus D.
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