Linear Algebra - Engineering Mathematics - Biotechnology Previous Year Questions

1

2013 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2013

If \(P = \begin{bmatrix} 1 & 1 \\ 2 & 2 \end{bmatrix}, Q = \begin{bmatrix} 2 & 1 \\ 2 & 2 \end{bmatrix}\) and \(R = \begin{bmatrix} 3 & 0 \\ 1 & 3 \end{bmatrix}\), which one of the following statements is TRUE?

A

PQ = PR

B

QR = RP

C

QP = RP

D

PQ = QR

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2

2013 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2013

One of the eigen values of \(P = \begin{bmatrix} 10 & -4 \\ 18 & -12 \end{bmatrix}\) is

A

2

B

4

C

6

D

8

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3

2013 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2013

The solution of the following set of equations is
\(x + 2y + 3z = 20\)
\(7x + 3y + z = 13\)
\(x + 6y + 2z = 0\)

A

\(x = -2, y = 2, z = 8\)

B

\(x = 2, y = -3, z = 8\)

C

\(x = 2, y = 3, z = -8\)

D

\(x = 8, y = 2, z = -3\)

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4

2013 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2013

All engineering students should learn mechanics, mathematics and how to do computation.
                 I                                   II                                     III                                     IV
Which of the above underlined parts of the sentence is not appropriate?

A

I

B

II

C

III

D

IV

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5

2014 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2014

The eigenvalues of \( A = \begin{bmatrix} 1 & -4 \\ 2 & -3 \end{bmatrix} \) are

A

2±i

B

-1, -2

C

-1±2i

D

non-existent

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6

2014 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2014

The solution for the following set of equations is,
\( 5x + 4y + 10z = 13 \)
\( x + 3y + z = 7 \)
\( 4x - 2y + z = 0 \)

A

x=2, y=1, z=1

B

x=1, y=2, z=0

C

x=1, y=0, z=2

D

x=0, y=1, z=2

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7

2014 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2014

The solution to the following set of equations is
\( 2x + 3y = 4 \)
\( 4x + 6y = 0 \)

A

x=0, y=0

B

x=2, y=0

C

4x=-6y

D

No solution

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8

2014 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2014

Match the items in Group I with Group II

A

P-1, Q-3, R-4, S-2

B

P-2, Q-4, R-3, S-1

C

P-3, Q-1, R-4, S-2

D

P-2, Q-4, R-1, S-3

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9

2016 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2016

The positive Eigen value of the following matrix is ______ .
\[\begin{bmatrix} 2 & 1 \\ 5 & -2 \end{bmatrix}\]

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10

2016 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2016

The value of determinant A given below is __________.
A = [5 16 81; 0 2 2; 0 0 16]

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11

2017 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2017

The value of \( c \) for which the following system of linear equations has an infinite number of solutions is _______.\[ \begin{bmatrix} 1 & 2 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} c \\ 4 \end{bmatrix} \]

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12

2018 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2018

The determinant of the matrix \(\begin{pmatrix} 4 & -6 \\ -3 & 2 \end{pmatrix}\) is __________

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13

2019 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2019

Matrix \(A = \begin{bmatrix} 0 & 6 \\ p & 0 \end{bmatrix}\) will be skew-symmetric when \(p =\) ________.

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14

2021 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2021

The determinant of matrix \( A = \begin{bmatrix} 1 & 1 & 1 & 1 \\ -1 & 1 & 1 & 1 \\ -1 & -1 & 1 & 1 \\ 1 & 1 & 1 & 3 \end{bmatrix} \) is ________.

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15

2022 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2022

If the eigenvalues of a 2×2 matrix \( P \) are 4 and 2, then the eigenvalues of the matrix \( P^{-1} \) are

A

0, 0

B

0.0625, 0.25

C

0.25, 0.5

D

2, 4

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16

2022 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2022

A 2×2 matrix P has an eigenvalue \(\lambda_1 = 2\) with eigenvector \(x_1 = \begin{pmatrix}1\\0\end{pmatrix}\) and another eigenvalue \(\lambda_2 = 5\), with eigenvector \(x_2 = \begin{pmatrix}1\\1\end{pmatrix}\). The matrix P is

A

\(\begin{pmatrix}2 & 0\\0 & 5\end{pmatrix}\)

B

\(\begin{pmatrix}2 & 3\\0 & 5\end{pmatrix}\)

C

\(\begin{pmatrix}1 & 1\\0 & 1\end{pmatrix}\)

D

\(\begin{pmatrix}1 & 1\\1 & 0\end{pmatrix}\)

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17

2024 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2024

A value of \( k \) for which the linear equations \( (k - 1)x + 3y = 0 \) and \( 2x + ky = 0 \) have a non-zero solution is ______.

A

1

B

2

C

3

D

4

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18

2024 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2024

Let \(\overrightarrow{OR}\) be the vector that is perpendicular to the vectors \(\overrightarrow{OP} = 2\hat{i} - 3\hat{j} + \hat{k}\) and \(\overrightarrow{OQ} = -2\hat{i} + \hat{j} + \hat{k}\). If the length of the vector \(\overrightarrow{OR}\) is \(\alpha \sqrt{3}\), then \(\alpha\) is ________.

A

3

B

4

C

5

D

6

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19

2024 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2024

If \(\vec{v} = \begin{pmatrix}2\\2\\2\end{pmatrix}\) is an eigenvector of the matrix \(\begin{pmatrix}1&2&3\\1&2&3\\1&2&3\end{pmatrix}\) corresponding to the non-zero eigenvalue, \(\lambda\), then the value of \(\lambda\) is ______.

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20

2025 · Biotechnology · Engineering Mathematics · Linear Algebra

Biotechnology (BT) 2025

The value of k, for which the linear equations 2x + 3y = 6 and 4x + 6y = 3k have at least one solution, is ______.
(Answer in integer)

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