Linear Algebra - Engineering Mathematics - Biomedical Engineering Previous Year Questions

1

2020 · Biomedical Engineering · Engineering Mathematics · Linear Algebra

Biomedical Engineering (BM) 2020

The eigenvalues of a 3 x 3 non-singular matrix P are 1, 2 and 3. The trace of matrix P⁻¹ (rounded off to two decimal places) is ________

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2

2021 · Biomedical Engineering · Engineering Mathematics · Linear Algebra

Biomedical Engineering (BM) 2021

The Trace and Determinant of a \(2 \times 2\) nonsingular matrix \(A\) are 12 and 32, respectively. The eigen values of \(A^{-1}\) are ____ and ____.

A

0.6, 0.8

B

0.25, 0.125

C

6, 16

D

1/12, 1/32

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3

2022 · Biomedical Engineering · Engineering Mathematics · Linear Algebra

Biomedical Engineering (BM) 2022

If the given matrices \( A = \begin{bmatrix} 3 & -2 \\ 4 & -2 \end{bmatrix} \) and \( I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \) satisfy \( A^2 = kA - 2I \), the value of coefficient \( k \) is ________.

A

1

B

2

C

0

D

4

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4

2023 · Biomedical Engineering · Engineering Mathematics · Linear Algebra

Biomedical Engineering (BM) 2023

\( Q = \begin{bmatrix} 1 & -2 \\ 2 & 1 \end{bmatrix} \) is a \( 2 \times 2 \) matrix. Which one of the following statements is TRUE?

A

Q is equal to its transpose.

B

Q is equal to its inverse.

C

Q is of full rank.

D

Q has linearly dependent columns.

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5

2023 · Biomedical Engineering · Engineering Mathematics · Linear Algebra

Biomedical Engineering (BM) 2023

Which one of the following vectors is an eigenvector corresponding to the eigenvalue = 1 for the matrix A? \( A = \begin{bmatrix} 1 & 1 & 0 \\ 1 & -1 & 0 \\ 1 & -1 & 1 \end{bmatrix} \)

A

[1 0 1]^T

B

[1 1 0]^T

C

[0 1 0]^T

D

[0 0 1]^T

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6

2024 · Biomedical Engineering · Engineering Mathematics · Linear Algebra

Biomedical Engineering (BM) 2024

If \(A = \begin{pmatrix} 1 & -1 \\ 2 & -2 \end{pmatrix}\), the eigenvalues of \(A\) are __________.

A

\(-1\) and \(0\).

B

\(-1\) and \(+1\).

C

\(-1\) and \(-1\).

D

\(+1\) and \(0\).

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7

2025 · Biomedical Engineering · Engineering Mathematics · Linear Algebra

Biomedical Engineering (BM) 2025

The determinant of a \(3 \times 3\) matrix \(M\) is 8. If every element of \(M\) is multiplied by \(-2\), the determinant of the modified matrix will be

A

-64

B

-16

C

8

D

64

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8

2025 · Biomedical Engineering · Engineering Mathematics · Linear Algebra

Biomedical Engineering (BM) 2025

The eigenvalues of the matrix \(\begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}\) are \_\_\_\_\_\_\_\_\_\_.

A

\(\cos\theta\) and \(\sin\theta\)

B

\(e^{i\theta}\) and \(e^{-i\theta}\), where \(i = \sqrt{-1}\)

C

\(\cos\theta\) and \(-\sin\theta\)

D

\(\cos 2\theta\) and \(\sin 2\theta\)

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9

2026 · Biomedical Engineering · Engineering Mathematics · Linear Algebra

Biomedical Engineering (BM) 2026

The eigenvalues of the matrix \( P = \begin{pmatrix} 1 & -2 \\ 3 & -4 \end{pmatrix} \) are

A

-1 and -2

B

1 and 2

C

0 and -1

D

0 and 1

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10

2026 · Biomedical Engineering · Engineering Mathematics · Linear Algebra

Biomedical Engineering (BM) 2026

An invertible \( n \times n \) matrix P satisfies \( P^3 = I \), where I is the identity matrix of size n. Which one of the following options is true?

A

\(P^5 = P \)

B

\(P^5 = P^{-1} \)

C

\(P^4 = P^{-1} \)

D

\(P^4 = P^2 \)

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11

2026 · Biomedical Engineering · Engineering Mathematics · Linear Algebra

Biomedical Engineering (BM) 2026

If \(\begin{pmatrix} 2 \\ a \end{pmatrix}\) is an eigenvector corresponding to the smallest eigenvalue of the matrix \(\begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix}\), the value of \(a\) is __________ (Answer in integer)

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