Master Matrix Operations: A Comprehensive Guide for Mechanical Engineering Students

Question 1

What is the trace of the matrix A = [2 5; 7 1]?

Accepted Answer

11

Answer

3

Answer

8

Answer

16

Question 2

Find the trace of the matrix: [[1, 2], [3, 4]]

Accepted Answer

5

Answer

7

Answer

1

Answer

2

Question 3

Find the inverse of the matrix B = [2, 3; -1, 2].

Accepted Answer

[0.4, -0.6; 0.2, 0.4]

Answer

[0.6, -0.4; -0.2, 0.4]

Answer

[2, 3; -1, 2]

Answer

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

Question 4

Find the inverse of the matrix: [1 2; 3 4]

Accepted Answer

[-2 1; 1.5 -0.5]

Answer

[-1 2; -3 4]

Answer

[1 2; -3 4]

Answer

[2 -1; -3 4]

Question 5

Which mathematical operation is not applicable to matrices?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 6

Which characteristic applies to a square matrix?

Accepted Answer

It has an equal number of rows and columns.

Answer

Its determinant is always positive.

Answer

Its inverse always exists.

Answer

It can be graphically represented as a plane.

Question 7

Identify the type of matrix multiplication NOT listed below:

Accepted Answer

Vector-matrix multiplication

Answer

Scalar multiplication

Answer

Matrix-matrix multiplication

Answer

Matrix-vector multiplication

Question 8

Which of the following operations cannot be performed on a matrix?

Accepted Answer

Division by a scalar

Answer

Addition with a scalar

Answer

Multiplication with a matrix

Answer

Taking the transpose

Question 9

Find the transpose of the matrix A = [1 2 3; 4 5 6]:

Accepted Answer

[1 4; 2 5; 3 6]

Answer

[3 2 1; 6 5 4]

Answer

[4 5; 2 3]

Answer

[6 5; 3 2]

Question 10

Which of the following matrices cannot be inverted?

Accepted Answer

[1 1; 1 1]

Answer

[1 0; 0 1]

Answer

[2 1; 1 2]

Answer

[0 1; 1 0]

Question 11

Find the adjoint of the matrix A = [2 -1; 3 4]:

Accepted Answer

[4 1; -3 -2]

Answer

[4 -1; -3 2]

Answer

[2 1; 3 4]

Answer

[4 3; -3 -2]

Question 12

Calculate the determinant of the matrix [2 3; 4 5].

Accepted Answer

5

Answer

-2

Answer

2

Answer

-5

Question 13

Identify the property of matrix multiplication that does not apply.

Accepted Answer

Commutative

Answer

Associative

Answer

Distributive

Answer

Closure

Question 14

Given matrices A = [[2, 4], [6, 8]] and B = [[1, 2], [3, 4]], what is A multiplied by B?

Accepted Answer

[[14, 20], [30, 44]]

Answer

[[4, 8], [12, 16]]

Answer

[[6, 12], [18, 24]]

Answer

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

Question 15

Which of the following matrices is considered elementary?

Accepted Answer

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

Answer

[[0, 2], [-3, 5]]

Answer

[[2, 4], [6, 8]]

Answer

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

Question 16

Which of the following matrices is singular?

Accepted Answer

[1 2; 0 0]

Answer

[0 1; 1 0]

Answer

[1 0; 0 1]

Answer

[2 1; 1 2]

Question 17

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

Accepted Answer

Commutative

Answer

Identity matrix exists

Answer

Associative

Answer

Distributive over scalar multiplication

Question 18

Which of the following operations is NOT allowed for matrices?

Accepted Answer

Division

Answer

Subtraction

Answer

Addition

Question 19

Name an application of matrices in mechanical engineering.

Accepted Answer

Solving systems of linear equations for structural analysis

Answer

Finding the area of surfaces

Answer

Calculating the volume of solids

Question 20

Consider the matrices: 
 A = [[1, 0, 2], [3, -1, 4]] 
 B = [[5, 2], [1, -3], [4, 6]] 
 Calculate A*B.

Accepted Answer

[[23, 14], [19, -11]]

Answer

[[32, 18], [26, -14]]

Answer

[[17, 10], [13, -7]]

Answer

[[11, 7], [9, -5]]

Question 21

Which of the following is a diagonal matrix?

Accepted Answer

[[2, 0, 0], [0, -3, 0], [0, 0, 4]]

Answer

[[1, 2, 3], [4, 5, 6], [7, 8, 9]]

Answer

[[1, 2, 0], [3, 0, 5], [0, 6, 7]]

Answer

[[0, 1, 2], [3, 0, 5], [6, 7, 0]]

Question 22

Identify the symmetric property in the following matrix:

Accepted Answer

A^T = A

Answer

A * A = A^2

Answer

A + A = 2A