Matrix Mathematics for Engineering: Interactive Quizzes and Practice

Question 1

Which property does NOT hold true for matrix multiplication?

Accepted Answer

Commutativity

Answer

Associativity

Answer

Distributivity over matrix addition

Answer

Existence of an identity matrix

Question 2

Which of the following operations cannot be performed on matrices?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication by a scalar

Question 3

What are the dimensions of a matrix with 5 rows and 3 columns?

Accepted Answer

5 x 3

Answer

3 x 5

Answer

3 x 1

Answer

1 x 3

Question 4

Which of the following matrices is the null matrix?

Accepted Answer

[[0, 0], [0, 0]]

Answer

[[1, 0], [0, 1]]

Answer

[[1, 1], [1, 1]]

Answer

[[2, 2], [2, 2]]

Question 5

Which of the following matrices is non-invertible?

Accepted Answer

[[0, 0], [0, 0]]

Answer

[[1, 2], [3, 4]]

Answer

[[1, 0], [0, 1]]

Answer

[[0, 1], [1, 0]]

Question 6

What is the inverse of the matrix [[2, 3], [-1, 2]]?

Accepted Answer

[[0.5, -0.75], [0.25, 1]]

Answer

[[2, 3], [-1, 2]]

Answer

[[1, -1], [-1, 2]]

Answer

[[2, -3], [-1, 2]]

Question 7

Which of the following properties does NOT apply to matrix multiplication?

Accepted Answer

Commutativity

Answer

Associativity

Answer

Distributivity over addition

Answer

Identity element

Question 8

Which of the following is NOT a property of matrices?

Accepted Answer

Matrices can be multiplied without considering their dimensions.

Answer

Matrices can be added and subtracted if they have the same dimensions.

Answer

Matrices can be multiplied by scalars.

Answer

Matrices can be used to solve systems of linear equations.

Question 9

What are the dimensions of a matrix with 3 rows and 5 columns?

Accepted Answer

3 by 5

Answer

5 by 3

Answer

3 by 3

Answer

5 by 5

Question 10

Which of the following matrices is the identity matrix?

Accepted Answer

1 0 | 0 1

Answer

0 1 | 1 0

Answer

1 1 | 1 1

Answer

0 0 | 0 0

Question 11

Which of the following is the transpose of the matrix 1 2 3 | 4 5 6?

Accepted Answer

1 4 | 2 5 | 3 6

Answer

4 1 | 5 2 | 6 3

Answer

1 2 3 | 4 5 6

Answer

3 2 1 | 6 5 4

Question 12

Calculate the inverse of the matrix $\begin{bmatrix} 2 & 3 \ -1 & 2 \ end{bmatrix}$.

Accepted Answer

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

Answer

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

Answer

$\begin{bmatrix} -2 & -3 \ 1 & -2 \ end{bmatrix}$

Answer

The matrix does not have an inverse.

Question 13

Which method for solving systems of linear equations involves row operations?

Accepted Answer

Gauss-Jordan elimination

Answer

Cramer's rule

Answer

Eigenvalue decomposition

Answer

Singular value decomposition

Question 14

Which geometric transformation is represented by the matrix $\begin{bmatrix} \cos\theta & -\sin\theta \ \sin\theta & \cos\theta \ end{bmatrix}$?

Accepted Answer

Rotation

Answer

Translation

Answer

Scaling

Answer

Reflection

Question 15

The roots of which mathematical expression are the eigenvalues of a matrix?

Accepted Answer

Characteristic equation

Answer

Determinant

Answer

Transpose

Answer

Inverse

Question 16

A matrix with only one non-zero row or column is called a:

Accepted Answer

Rank-1 matrix

Answer

Zero matrix

Answer

Diagonal matrix

Answer

Identity matrix

Question 17

Which property does NOT apply to matrix multiplication?

Accepted Answer

Commutative Property

Answer

Associative Property

Answer

Distributive Property

Answer

Identity Matrix Property

Question 18

What is the trace of the matrix [[a, b], [c, d]]?

Accepted Answer

a + d

Answer

a + b + c + d

Answer

b + c

Answer

a - d

Question 19

Which type of matrix is used to represent rotations in 3D space?

Accepted Answer

Rotation matrix

Answer

Square matrix

Answer

Identity matrix

Answer

Symmetric matrix

Question 20

What is the adjoint of the matrix [[1, 2], [3, 4]]?

Accepted Answer

[[4, -2], [-3, 1]]

Answer

[[-2, -3], [1, 4]]

Answer

[[2, -3], [-1, 4]]

Answer

[[1, -2], [3, -4]]

Question 21

Which operation is not applicable to matrices?

Accepted Answer

Dividing one matrix by another

Answer

Adding matrices of the same order

Answer

Multiplying a matrix by a scalar

Answer

Finding the product of two compatible matrices

Question 22

How are matrices used in real-world applications? Choose three examples from the following fields:

Accepted Answer

Computer Graphics:  Transforming 3D objects.

Accepted Answer

Engineering: Analyzing the structure of bridges.

Accepted Answer

Physics: Describing particle motion in quantum mechanics.

Question 23

What matrix operation is not defined for matrices of different sizes?

Accepted Answer

Multiplication

Answer

Addition

Answer

Subtraction

Answer

Exponentiation

Question 24

What is the determinant of the matrix [[2 3], [4 5]]?

Accepted Answer

10

Answer

-2

Answer

2

Answer

-10

Question 25

Identify the identity matrix of order 3.

Accepted Answer

[[1 0 0], [0 1 0], [0 0 1]]

Answer

[[0 1 0], [1 0 0], [0 0 1]]

Answer

[[1 0 0], [0 0 1], [0 1 0]]

Answer

[[0 0 1], [0 1 0], [1 0 0]]

Question 26

Find the transpose of the matrix [[2 3 4], [5 6 7]]

Accepted Answer

[[2 5], [3 6], [4 7]]

Answer

[[2 3 4], [5 6 7]]

Answer

[[7 6 5], [4 3 2]]

Answer

[[7 4 2], [6 3 5]]

Question 27

Which of the following systems of linear equations is represented by the augmented matrix [[1 2 3] | [4 5 6]]?

Accepted Answer

x + 2y + 3z = 4

Answer

x + 2y + 3z = 6

Answer

2x + 5y + 6z = 4

Answer

x + y + z = 4

Question 28

Which of the following matrices is symmetric?

Accepted Answer

[[1 2], [2 1]]

Answer

[[1 3], [4 2]]

Answer

[[2 1], [4 3]]

Answer

[[2 3], [4 3]]

Question 29

Calculate the determinant of the matrix C = [[3, 2], [1, -1]].

Accepted Answer

-5

Answer

-1

Answer

5

Answer

2

Question 30

Find the inverse of the matrix D = [[1, 2], [0, 1]].

Accepted Answer

[[1, -2], [0, 1]]

Answer

[[1, 0], [-2, 1]]

Answer

[[1, 2], [0, 1]]

Answer

[[0, 1], [1, 2]]

Question 31

In the matrix equation AX = B representing a system of linear equations, what does X represent?

Accepted Answer

The column matrix of variables

Answer

The solution matrix

Answer

The constant matrix

Answer

The coefficient matrix

Question 32

Which of the following properties does NOT hold true for matrix multiplication?

Accepted Answer

Commutative Property (AB = BA)

Answer

Associative Property (A(BC) = (AB)C)

Answer

Distributive Property (A(B+C) = AB + AC)

Answer

Identity Property (AI = IA = A)

Question 33

A square matrix is considered singular if its determinant is:

Accepted Answer

Zero

Answer

Positive

Answer

Negative

Answer

One

Question 34

A matrix with an equal number of rows and columns is called a:

Accepted Answer

Square Matrix

Answer

Column Matrix

Answer

Row Matrix

Answer

Diagonal Matrix

Question 35

Given matrices A = [[2, 1], [0, 3]] and B = [[1, -2], [4, 1]], calculate A + B.

Accepted Answer

[[3, -1], [4, 4]]

Answer

[[1, 2], [-4, 2]]

Answer

[[3, 3], [4, 4]]

Answer

[[2, -2], [0, 3]]

Question 36

Determine the inverse of matrix F = [[1, 2], [3, 4]].

Accepted Answer

[[-2, 1], [1.5, -0.5]]

Answer

[[1/1, 1/2], [1/3, 1/4]]

Answer

Not invertible

Answer

[[4, -2], [-3, 1]]

Question 37

The system of equations 2x - y = 5 and x + 3y = 4 can be represented in matrix form as:

Accepted Answer

[[2, -1], [1, 3]] [[x], [y]] = [[5], [4]]

Answer

[[x], [y]] [[2, -1], [1, 3]] = [[5], [4]]

Answer

[[2, 1], [-1, 3]] [[x], [y]] = [[5], [4]]

Answer

[[2, -1], [1, 3]] [[5], [4]] = [[x], [y]]

Question 38

The transformation matrix T = [[0, 1], [-1, 0]] represents what type of geometric transformation?

Accepted Answer

Rotation by 90 degrees clockwise

Answer

Enlargement by a scale factor of 2

Answer

Reflection in the x-axis

Answer

Translation by 2 units to the right

Question 39

Which of the following is NOT a property of matrix multiplication?

Accepted Answer

Commutative property: AB = BA

Answer

Associative property: A(BC) = (AB)C

Answer

Distributive property: A(B + C) = AB + AC

Answer

Identity property: AI = IA = A (where I is the identity matrix)

Question 40

A matrix with the same number of rows and columns is called a:

Accepted Answer

Square matrix

Answer

Column matrix

Answer

Row matrix

Answer

Rectangular matrix