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Questions › UGC-NET › UGC-NET 2023 › Q60
2 marksMathematics › Vector spaces, rank and eigenvalues › Eigenvalues and eigenvectorsHardabout 2 min

UGC-NET 2023 Question 60: Vector spaces, rank and eigenvalues

Consider a matrix A = [[3, 5],[-2, -4]]. Consider the following statements on the characteristic polynomial, Eigenvalues and Eigenvectors.

(A) The characteristic polynomial is lambda^2 + lambda - 2.

(B) The characteristic polynomial is lambda^2 - 2*lambda - 4 and the Eigenvalues are 2 and 1.

(C) The characteristic polynomial is lambda^2 - lambda + 2 and the Eigenvalues are 1 and 2.

(D) The Eigenvalues are -2 and 1.

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Vector spaces, rank and eigenvalues has come up 41 times in 6 exams since 2008.

What this question tests

This question is on Eigenvalues and eigenvectors, part of Vector spaces, rank and eigenvalues in Mathematics.

The scalars and directions a matrix only stretches, and what they say about invertibility and trace.

TestStop has 6 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2022 · Q41The sum of the eigenvalues of the square matrix [1 1 3; 1 5 1; 3 1 1] is _ (in integer).
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