Linear Algebra - Engineering Mathematics - Agricultural Engineering Previous Year Questions

1

2008 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2008

Eigenvalues of the matrix \(\begin{pmatrix} 2 & 1 \\ 2 & 3 \end{pmatrix}\) are

A

1 and 2

B

1 and 3

C

1 and 4

D

2 and 3

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2

2009 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2009

Inverse of the matrix \(\begin{pmatrix} 2 & 3 \\ 2 & 1 \end{pmatrix}\) is

A

\(\begin{pmatrix} -0.5 & 0.75 \\ 0.5 & -0.25 \end{pmatrix}\)

B

\(\begin{pmatrix} -0.25 & 0.5 \\ -0.5 & 0.75 \end{pmatrix}\)

C

\(\begin{pmatrix} -0.25 & 0.75 \\ 0.5 & -0.5 \end{pmatrix}\)

D

\(\begin{pmatrix} -0.25 & -0.5 \\ 0.75 & 0.5 \end{pmatrix}\)

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3

2010 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2010

A system of equations represented as
\( \begin{bmatrix} 1 & -1 & 2 \\ 2 & 1 & -4 \\ 1 & 3 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 4 \\ 1 \\ 3 \end{bmatrix} \) is

A

consistent and has unique solution

B

inconsistent and has no solution

C

consistent and has infinite solutions

D

inconsistent and has unique solution

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4

2011 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2011

A square matrix [A] will be lower triangular if and only if (\(a_{MN}\) represents an element of \(M^{th}\) row and \(N^{th}\) column of the matrix)

A

\(a_{MN} = 0, N>M\)

B

\(a_{MN} = 0, M>N\)

C

\(a_{MN} \neq 0, M>N\)

D

\(a_{MN} \neq 0, N>M\)

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5

2014 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2014

The eigenvalues of the matrix A = [ 2 2 ; -1 5 ] are

A

1 and 2

B

2 and 3

C

3 and 4

D

4 and 5

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6

2014 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2014

Consider the following set of linear equations
x₁ + x₂ + x₃ = 6
2x₁ + 2x₂ + 3x₃ = 14
3x₁ + x₂ + 2x₃ = 14
The solution for this set exists only when the value of x₂ is ______.

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7

2015 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2015

Inverse of the matrix \(\begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix}\) is

A

\(\begin{bmatrix} 0.1 & -0.4 \\ -0.3 & 0.2 \end{bmatrix}\)

B

\(\begin{bmatrix} 0.3 & -0.2 \\ -0.1 & 0.4 \end{bmatrix}\)

C

\(\begin{bmatrix} 0.3 & -0.1 \\ -0.2 & 0.4 \end{bmatrix}\)

D

\(\begin{bmatrix} 0.4 & -0.2 \\ -0.1 & 0.3 \end{bmatrix}\)

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8

2016 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2016

Eigen values of the matrix \( \begin{bmatrix} 5 & 3 \\ 1 & 4 \end{bmatrix} \) are

A

-6.3 and -2.7

B

-2.3 and -6.7

C

6.3 and 2.7

D

2.3 and 6.7

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9

2017 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2017

Matrix \(\begin{bmatrix} 0 & 0.5 & 1.5 \\ -0.5 & 0 & 2.5 \\ -1.5 & -2.5 & 0 \end{bmatrix}\) is a

A

Diagonal matrix

B

Orthogonal matrix

C

Symmetric matrix

D

Skew-symmetric matrix

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10

2017 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2017

Characteristic equation of the matrix \(\begin{bmatrix} 2 & \sqrt{2} \\ \sqrt{2} & 1 \end{bmatrix}\) with Eigen value \(\lambda\) is

A

\(\lambda^2 + 3\lambda + 4 = 0\)

B

\(\lambda^2 + 3\lambda - 2 = 0\)

C

\(\lambda^2 - 3\lambda = 0\)

D

\(\lambda^2 + 3\lambda = 0\)

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11

2018 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2018

Rank of a matrix \[\begin{bmatrix} 5 & 3 & -3 & -1 \\ 3 & 2 & -2 & -1 \\ 2 & -1 & 2 & 8 \end{bmatrix}\] is

A

1

B

2

C

3

D

4

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12

2020 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2020

A linear system of equations has \( n \) unknowns. The ranks of the coefficient matrix and the augmented matrix of the linear system of equations are \( r_1 \) and \( r_2 \), respectively. The condition for the equations to be consistent with a unique solution is

A

\(r_1 < r_2 < n \)

B

\(r_1 = r_2 = n \)

C

\(r_1 = r_2 < n \)

D

\(r_1 \neq r_2 > n \)

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13

2020 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2020

If one of the two Eigenvalues of a matrix \(\begin{bmatrix} 3 & 2 \\ 2 & 1 \end{bmatrix}\) is 4.236, then the other Eigenvalue (round off to 3 decimal places) is ______________.

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14

2021 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2021

Trace of the matrix \(\begin{bmatrix} 3 & 2 & 1 & 4 \\ 5 & 7 & 8 & 1 \\ 2 & 4 & 6 & 7 \\ 9 & 6 & 4 & 2 \end{bmatrix}\) is ______. [in integer]

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15

2021 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2021

Summation of eigenvalues of a matrix \[ \begin{bmatrix} 4 & 1 \\ 3 & 6 \end{bmatrix} \] is ______. [round off to the nearest integer]

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16

2022 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2022

Determinant of a matrix remains unaltered if ______.

A

its columns and rows are interchanged

B

two parallel lines are identical

C

two parallel lines intersect

D

each element of a line is multiplied by the same factor

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17

2022 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2022

The matrix \(\begin{bmatrix} (3 – x) & 2 & 2 \\ 2 & (4 – x) & 1 \\ -2 & -4 & (-1 – x) \end{bmatrix}\) is singular for the following values of x

A

x = 0 and x = 3

B

x = 0 and x = –3

C

x = 0 and x = 6

D

x = 0 and x = –6

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18

2023 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2023

If A and B are square matrices of order 3 such that \(|A| = -1\), \(|B| = 3\), then \(|3AB|\) equals

A

-81

B

-27

C

-9

D

81

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19

2023 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2023

If A = \[\begin{bmatrix} 1 & -1 \\ 2 & -1 \end{bmatrix}\, B = \[\begin{bmatrix} a & 1 \\ b & -1 \end{bmatrix}\] and (A + B)² = A² + B², then the values of a and b are:

A

a = 4, b = 1

B

a = 1, b = 4

C

a = 0, b = 4

D

a = 2, b = 4

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20

2024 · Agricultural Engineering · Engineering Mathematics · Linear Algebra

Agricultural Engineering (AG) 2024

\[ [P] = \begin{bmatrix} 2 & 3 & 7 \\ 4 & 1 & 5 \end{bmatrix} \] and \[ [Q] = \begin{bmatrix} 8 & 11 & 9 \\ 12 & 6 & 13 \end{bmatrix} \] are two matrices. The matrix \[ [P]^T [Q] \] is __________.

A

\(\begin{bmatrix} 64 & 36 & 116 \\ 46 & 39 & 107 \\ 70 & 40 & 128 \end{bmatrix}\)

B

\(\begin{bmatrix} 64 & 46 & 70 \\ 36 & 39 & 40 \\ 116 & 107 & 128 \end{bmatrix}\)

C

\(\begin{bmatrix} 112 & 113 \\ 88 & 89 \end{bmatrix}\)

D

\(\begin{bmatrix} 112 & 88 \\ 113 & 89 \end{bmatrix}\)

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