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Questions › IIT JAM › IIT JAM 2024 › Q37
2 marksMathematics › Vector spaces, rank and eigenvalues › Eigenvalues and eigenvectorsHardabout 3 min

IIT JAM 2024 Question 37: Vector spaces, rank and eigenvalues

Let M=(α−6−11)M = \begin{pmatrix} \alpha & -6 \\ -1 & 1 \end{pmatrix}M=(α−1​−61​), α∈R\alpha \in Rα∈R. If the eigenvalues of MMM are β\betaβ and 444, which of the following is/are CORRECT?

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Answer and worked solution

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Plain-text version

Let M = [α -6; -1 1], α ∈ R. If the eigenvalues of M are β and 4, which of the following is/are CORRECT? (A) α + β = 1 (B) An eigenvector corresponding to β is [2, 1]ᵀ (C) The rank of the matrix M is 2 (D) The matrix M² + M is invertible

Also written as: Let M = [alpha -6; -1 1], alpha in R. If the eigenvalues of M are beta and 4, which of the following is/are CORRECT?

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).
Take this paper as a timed mockMore on Eigenvalues and eigenvectors

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