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Previous year question hub

Eigenvalues and Canonical Forms - Linear Algebra - Mathematics Previous Year Questions

Practice Eigenvalues and Canonical Forms - Linear Algebra - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

20Papers
20Years
56Questions
1Topics

Eigenvalues and Canonical Forms question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Eigenvalues and Canonical Forms. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 40 71.4%
Easy 11 19.6%
Hard 5 8.9%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

MCQ 28 50%
Numerical Answer Type (NAT) 21 37.5%
MSQ 6 10.7%
Fill in the blanks 1 1.8%

Subject weightage

Top subjects by unique question coverage.

Mathematics
56 Qs

Most asked topics

Top topics across the included previous year papers.

Linear Algebra
56 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Eigenvalues and Canonical Forms
56 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

Mathematics (MA) 2026
4 Qs
Mathematics (MA) 2025
5 Qs
Mathematics (MA) 2024
4 Qs
Mathematics (MA) 2023
5 Qs
Mathematics (MA) 2022
2 Qs
Mathematics (MA) 2021
2 Qs
Mathematics (MA) 2020
1 Qs
Mathematics (MA) 2019
2 Qs
Mathematics (MA) 2018
3 Qs
Mathematics (MA) 2017
3 Qs
Mathematics (MA) 2016
4 Qs
Mathematics (MA) 2015
2 Qs
Mathematics (MA) 2014
2 Qs
Mathematics (MA) 2013
3 Qs
Mathematics (MA) 2012
2 Qs
Mathematics (MA) 2011
3 Qs
Mathematics (MA) 2010
1 Qs
Mathematics (MA) 2009
3 Qs
Mathematics (MA) 2008
2 Qs
Mathematics (MA) 2007
3 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
Mathematics (MA) 202620264View paper
Mathematics (MA) 202520255View paper
Mathematics (MA) 202420244View paper
Mathematics (MA) 202320235View paper
Mathematics (MA) 202220222View paper
Mathematics (MA) 202120212View paper
Mathematics (MA) 202020201View paper
Mathematics (MA) 201920192View paper
Mathematics (MA) 201820183View paper
Mathematics (MA) 201720173View paper
Mathematics (MA) 201620164View paper
Mathematics (MA) 201520152View paper
Mathematics (MA) 201420142View paper
Mathematics (MA) 201320133View paper
Mathematics (MA) 201220122View paper
Mathematics (MA) 201120113View paper
Mathematics (MA) 201020101View paper
Mathematics (MA) 200920093View paper
Mathematics (MA) 200820082View paper
Mathematics (MA) 200720073View paper

All Eigenvalues and Canonical Forms previous year questions

Practice every matching question in batches of 20, with every available option.

1
2008 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2008
Let \(M = \begin{bmatrix} 1 & 0 & 0 \\ 0 & \cos \theta & -\sin \theta \\ 0 & \sin \theta & \cos \theta \end{bmatrix}\), where \(0 < \theta < \frac{\pi}{2}\). Let \(V = \{u \in \mathbb{R}^3 : M u^T = u^T\}\). Then the dimension of \(V\) is
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2
2008 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2008
The number of linearly independent eigenvectors of the matrix \(\begin{bmatrix} 2 & 2 & 0 & 0 \\ 2 & 1 & 0 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 1 & 4 \end{bmatrix}\) is
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3
2009 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2009
The minimal polynomial associated with the matrix \begin{bmatrix} 0 & 0 & 3 \\ 1 & 0 & 2 \\ 0 & 1 & 1 \end{bmatrix} is
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4
2009 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2009
If \(A = \begin{pmatrix} 1 & 0 & 0 \\ i & \frac{-1+i\sqrt{3}}{2} & 0 \\ 0 & 1+2i & \frac{-1-i\sqrt{3}}{2} \end{pmatrix}\), then the trace of \(A^{102}\) is
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5
2009 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2009
Which of the following matrices is NOT diagonalizable ?
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6
2010 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2010
If a \( 3 \times 3 \) real skew-symmetric matrix has an eigenvalue \( 2i \), then one of the remaining eigenvalues is
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7
2011 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2011
The distinct eigenvalues of the matrix \[\begin{bmatrix} 1 & 1 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 0 \end{bmatrix}\] are
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8
2011 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2011
The minimal polynomial of the matrix \[\begin{bmatrix} 3 & 3 & 0 \\ 3 & 3 & 0 \\ 0 & 0 & 6 \end{bmatrix}\] is
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9
2011 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2011
Let \( T : \mathbb{R}^4 \to \mathbb{R}^4 \) be defined by \( T(x,y,z,w) = (x + y + 5w, x + 2y + w, -z + 2w, 5x + y + 2z). \) The dimension of the eigenspace of T is
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10
2012 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2012
Let \(\alpha=e^{2\pi i/5}\) and the matrix \[M=\begin{bmatrix} 1 & \alpha & \alpha^2 & \alpha^3 & \alpha^4 \\ 0 & \alpha & \alpha^2 & \alpha^3 & \alpha^4 \\ 0 & 0 & \alpha^2 & \alpha^3 & \alpha^4 \\ 0 & 0 & 0 & \alpha^3 & \alpha^4 \\ 0 & 0 & 0 & 0 & \alpha^4 \end{bmatrix}.\] Then the trace of the matrix \(I+M+M^2\) is
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11
2012 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2012
If \(A=\begin{bmatrix} 1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix}\), then \(A^{50}\) is
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12
2013 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2013
The possible set of eigen values of a \(4\times 4\) skew-symmetric orthogonal real matrix is
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13
2013 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2013
Let \(P\) be a \(2 \times 2\) complex matrix such that \(\text{trace}(P) = 1\) and \(\text{det}(P) = -6\). Then, \(\text{trace}(P^4 - P^3)\) is ______
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14
2013 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2013
Let \(V\) be a vector space of dimension \(m \ge 2\). Let \(T: V \to V\) be a linear transformation such that \(T^{n+1} = 0\) and \(T^n \neq 0\) for some \(n \ge 1\). Then which of the following is necessarily TRUE?
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15
2014 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2014
Let \(A \in M_3(\mathbb{R})\) be such that \(\det(A-I) = 0\), where \(I\) denotes the 3×3 identity matrix. If the \(\text{trace}(A) = 13\) and \(\det(A) = 32\), then the sum of squares of the eigenvalues of \(A\) is ______________
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16
2014 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2014
Let \(X = \begin{bmatrix} 2 & 0 & -3 \\ 3 & -1 & -3 \\ 0 & 0 & -1 \end{bmatrix}\). A matrix \(P\) such that \(P^{-1}XP\) is a diagonal matrix, is
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17
2015 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2015
Let \(T : \mathbb{R}^4 \to \mathbb{R}^4\) be a linear map such that the null space of \(T\) is \[(x, y, z, w) \in \mathbb{R}^4 : x + y + z + w = 0\] and the rank of \((T - 4I_4)\) is 3. If the minimal polynomial of \(T\) is \(x(x - 4)^\alpha\), then \(\alpha\) is equal to ________
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18
2015 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2015
Let \(M\) be an invertible Hermitian matrix and let \(x, y \in \mathbb{R}\) be such that \(x^2 < 4y\). Then
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19
2016 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2016
Consider the following statements P and Q:
(P): If M = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 4 \\ 1 & 3 & 9 \end{bmatrix}, then M is singular.
(Q): Let S be a diagonalizable matrix. If T is a matrix such that S + 5T = Id, then T is diagonalizable.
Which of the above statements hold TRUE?
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20
2016 · Mathematics · Linear Algebra · Eigenvalues and Canonical Forms
Mathematics (MA) 2016
Consider a real vector space V of dimension n and a non-zero linear transformation T : V → V. If dimension(T(V)) < n and T2 = λT, for some λ ∈ ℝ\{0}, then which of the following statements is TRUE?
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Showing 20 of 56 questions