Consider the matrix as given below. 1 & 2 & 3 0 & 4 & 7 0 & 0 & 3 Which one of the following options provides the CORRECT values of the eigenvalues of the matrix?
Topic-wise GATE CS PYQs with verified steps
GATE CSE 2011 · Q40
Time
Select one answerSingle correct
Solution
Official answer: A) 1, 4, 3
Linear AlgebraThe given matrix is an upper triangular matrix:
For any upper triangular, lower triangular, or diagonal matrix, the eigenvalues are simply the elements on the principal diagonal.
The diagonal elements of matrix are and .
Therefore, the eigenvalues of the matrix are , corresponding to option (A).
Try the question first, then check your work.
Examiner trap
Recall that the eigenvalues of any triangular matrix are simply its principal diagonal elements.
This Linear Algebra previous year question is Q40 of the GATE CSE 2011 paper. Find more GATE CSE PYQs on Linear Algebra in Engineering Mathematics, or browse all GATE CSE PYQs.
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Linear Algebra has 46 GATE CSE PYQs across 26 papers from 2011 to 2026. 10 of them are 2-mark MCQs like this one, and it is the only one in GATE CSE 2011.
How GATE tests Linear AlgebraIndependent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.