Official PYQ · 2017Set 1 · Q1Linear AlgebraMCQ1 mark

GATE EC 2017 Set 1 Q1 — Linear Algebra

Consider the 5 $\times$ 5 matrix

$\begin{bmatrix} 1&2&3&4&5\\ 5&1 &2& 3 &4\\ 4&5&1&2&3\\ 3&4&5&1&2\\ 2&3&4&5&1 \end{bmatrix}$

It is given that A has only one real eigenvalue. Then the real eigenvalue of A is

View answer

Answer: C

Worked explanation not available yet.

Free practice · Your answers on this page are not saved.

Published 10 Oct 2026

Report a correction

GATE EC · 2026Linear Algebra
Consider the matrix $\mathrm{M}=\left[\begin{array}{ccc}2 & 1 & 1 \\ 1 & 3 & 0 \\ -1 & a & b\end{array}\right]$ . Which of the following options is/ are TRUE if $\operatorname{det}(\mathrm{M}) \neq 0 ?$
MSQ · 1 mark
GATE EC · 2025Linear Algebra
Consider the matrix $A$ below: $A=\left[\begin{array}{llll} 2 & 3 & 4 & 5 \\ 0 & 6 & 7 & 8 \\ 0 & 0 & \alpha & \beta \\ 0 & 0 & 0 & \gamma \end{array}\right]$ For which of the following combinations of $\alpha, \beta$ , and $\gamma$ , is the rank of $A$ at least three? Only (i), (iii), and (iv) Only …
MCQ · 1 mark
GATE EC · 2024Linear Algebra
Let $\mathbb{R}$ and $\mathbb{R}^{3}$ denote the set of real numbers and the three dimensional vector space over it, respectively. The value of $\alpha$ for which the set of vectors …
NAT · 1 mark
GATE EC · 2024Linear Algebra
Consider the matrix $\left[\begin{array}{ll}1 & k \\ 2 & 1\end{array}\right]$ , where $k$ is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix?
MSQ · 2 marks
GATE EC · 2023Linear Algebra
Let $v_1=\left[\begin{array}{l}1 \\ 2 \\ 0\end{array}\right]$ and $v_2=\left[\begin{array}{l}2 \\ 1 \\ 3\end{array}\right]$ be two vectors. The value of the coefficient $\alpha$ in the expression $v_1=\alpha v_2+e$ , which minimizes the length of the error vector $e$ , is
MCQ · 1 mark
GATE EC · 2023Linear Algebra
Let the sets of eigenvalues and eigenvectors of a matrix $B$ be $\left\{\lambda_k \mid 1 \leq k \leq n\right\}$ and $\left\{v_k \mid 1 \leq k \leq n\right\}$ , respectively. For any invertible matrix $P$ , the sets of eigenvalues and eigenvectors of the matrix $A$ , where $B=P^{-1} A P$ , respectively, are
MCQ · 1 mark

Browse this topic

More Linear Algebra questions

GATE EC 2017 Set 1 Q1 — Linear Algebra

Related questions