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Questions › IIT JAM › IIT JAM 2023 › Q55
2 marksMathematics › Vector spaces, rank and eigenvalues › Eigenvalues and eigenvectorsHardabout 3 min

IIT JAM 2023 Question 55: Vector spaces, rank and eigenvalues

Let M=(k111k111k)M=\begin{pmatrix}k&1&1\\1&k&1\\1&1&k\end{pmatrix}M=​k11​1k1​11k​​ and I3I_3I3​ the identity. If the rank of 10I3−M10I_3-M10I3​−M is 222, then kkk is equal to ________ (in integer).

Answer and worked solution

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Plain-text version

Let M=[k 1 1; 1 k 1; 1 1 k] and I₃ the identity. If the rank of 10I₃-M is 2, then k is equal to (in integer).

Also written as: Let M=[k 1 1; 1 k 1; 1 1 k] and I_3 the identity. If the rank of 10I_3-M is 2, then k is equal to (in integer).

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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Question from the IIT JAM 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.