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Linear Algebra

GATE CSE 2011 · Q40

MCQ2 marksEasy

Time

Consider the matrix as given below. [123047003]\begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 7 \\ 0 & 0 & 3 \end{bmatrix} Which one of the following options provides the CORRECT values of the eigenvalues of the matrix?

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Solution

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Official answer: A) 1, 4, 3

Linear Algebra

The given matrix is an upper triangular matrix:

A=[123047003]A = \begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 7 \\ 0 & 0 & 3 \end{bmatrix}

For any upper triangular, lower triangular, or diagonal matrix, the eigenvalues are simply the elements on the principal diagonal.

The diagonal elements of matrix AA are 1,4,1, 4, and 33.

Therefore, the eigenvalues of the matrix are 1,4,31, 4, 3, corresponding to option (A).

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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 in GATE CSE

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.

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GateAI solution cardGATE CSE 2011 · Q40 · MCQ

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?

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