Master Matrix Math: Conquer Matrices with Confidence

Question 1

Which of the following matrices is the transpose of: [[m, n], [p, q]]

Accepted Answer

[[m, p], [n, q]]

Answer

[[p, m], [q, n]]

Answer

[[n, p], [m, q]]

Answer

[[q, p], [n, m]]

Question 2

Which of the following is a square matrix?

Accepted Answer

An mxn matrix where m = n

Answer

An mxn matrix where m != n

Answer

An nxn matrix where n is odd

Answer

An mxm matrix where m is even

Question 3

Which of the following matrices is symmetric?

Accepted Answer

A square matrix that is equal to its transpose

Answer

A rectangular matrix that has the same elements on both sides of the main diagonal

Answer

A square matrix that has all its elements equal to zero

Answer

A rectangular matrix that has the same number of rows and columns

Question 4

Find the trace of the matrix: [[a, b], [-c, d]]

Accepted Answer

a + d

Answer

a - d

Answer

b + c

Answer

b - c

Question 5

Distinguish between a square and a rectangular matrix.

Accepted Answer

A square matrix has an equal number of rows and columns, unlike a rectangular matrix.

Answer

A rectangular matrix has an equal number of rows and columns, unlike a square matrix.

Answer

Square and rectangular matrices both have the same number of rows and columns.

Answer

There is no distinction between a square matrix and a rectangular matrix.

Question 6

If the matrix A has a dimension of 3x2 and the matrix B has a dimension of 2x4, what is the dimension of the product matrix AB?

Accepted Answer

3x4

Answer

3x2

Answer

2x3

Answer

2x4

Question 7

Which of the following matrices is diagonal?

Accepted Answer

[[1 0; 0 2]

Answer

[[1 2; 3 4]

Answer

[[1 2; 0 4]

Answer

[[0 1; 2 3]

Question 8

Identify the invalid operation for matrices.

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 9

Determine the determinant of the matrix A = [2 3] [5 7].

Accepted Answer

11

Answer

1

Answer

23

Answer

31

Question 10

Which matrix equation represents the system of equations: 2x1 + x2 = 5, 3x1 + 4x2 = 7

Accepted Answer

Ax = b, where A = [2 1] [3 4], x = [x1] [x2], and b = [5] [7]

Answer

Ax = b, where A = [2 1] [3 4], x = [x2] [x1], and b = [7] [5]

Answer

Ax = b, where A = [1 2] [3 4], x = [x1] [x2], and b = [5] [7]

Answer

Ax = b, where A = [1 2] [4 3], x = [x1] [x2], and b = [7] [5]

Question 11

Identify the diagonal matrix from the following options:

Accepted Answer

[1 0 0] [0 2 0] [0 0 3]

Answer

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

Answer

[1 0 2] [0 2 0] [0 0 4]

Answer

[1 2 4] [5 6 8] [9 10 12]

Question 12

Which of the following operations cannot be performed on matrices?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 13

What is the order of a matrix defined by?

Accepted Answer

The number of rows and columns

Answer

The sum of its elements

Answer

The product of its elements

Answer

The determinant of the matrix

Question 14

In a matrix equation of the form Ax = b, what does the matrix A represent?

Accepted Answer

The coefficients of the variables

Answer

The variables themselves

Answer

The constants on the right-hand side

Answer

The solution to the system

Question 15

What does the determinant of a matrix represent?

Accepted Answer

The area of the parallelogram formed by the matrix's column vectors

Answer

The volume of the parallelepiped formed by the matrix's column vectors

Answer

The number of solutions to the matrix equation Ax = 0

Answer

The inverse of the matrix

Question 16

What is the key characteristic of the transpose of a matrix A, denoted as AT?

Accepted Answer

Its rows become columns and vice versa

Answer

Its elements are multiplied by -1

Answer

Its determinant is negated

Answer

Its inverse is also its transpose

Question 17

Which operation is undefined for matrices?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 18

Given matrices A = [2 1] and B = [3 5], calculate the matrix A + B.

Accepted Answer

[5 6]

Answer

[6 5]

Answer

[5 0]

Answer

[0 5]

Question 19

The dimensions of the product AB are determined by the:

Accepted Answer

Number of rows in A and number of columns in B

Answer

Number of columns in A and number of rows in B

Answer

Number of rows in B and number of columns in A

Answer

Number of columns in B and number of rows in A

Question 20

Find the determinant of the matrix [[2 1], [3 4]]?

Accepted Answer

5

Answer

-5

Answer

1

Answer

-1

Question 21

Identify the diagonal matrix with a non-zero determinant:

Accepted Answer

2 0 0
0 2 0
0 0 2

Answer

1 2 3
0 5 0
0 0 9

Answer

1 2 3
4 5 6
7 8 9

Question 22

What is the relationship between the determinant of a non-singular matrix |A| and the determinant of its inverse |A-1|?

Accepted Answer

|A| multiplied by |A-1| equals 1

Answer

|A| equals |A-1|

Answer

|A| minus |A-1| equals 0

Question 23

In computer graphics, matrices are used to:

Accepted Answer

Represent and manipulate transformations

Answer

Store lighting and shading information

Answer

Calculate object lengths and angles

Answer

Generate object textures

Question 24

Find the sum of the matrices [1 2] and [3 4].

Accepted Answer

[4 6]

Answer

[2 4]

Answer

[2 6]

Answer

[4 8]

Question 25

Which system of equations is represented by the matrix equation [1 2; 3 4][x y] = [5 6]?

Accepted Answer

x + 2y = 5, 3x + 4y = 6

Answer

x + 2y = 6, 3x + 4y = 5

Answer

x - 2y = 5, 3x - 4y = 6

Answer

x - 2y = 6, 3x - 4y = 5

Question 26

Which of the following matrices is a scalar matrix?

Accepted Answer

[1 0; 0 1]

Answer

[1 2; 3 4]

Answer

[2 3; 4 5]

Answer

[0 1; 1 0]

Question 27

In a system of equations Ax = b, where A is a matrix with rank r, if r is less than the number of variables, what can be said about the system?

Accepted Answer

It has either no solution or infinitely many solutions.

Answer

It has a unique solution for any b.

Answer

It is always consistent.

Answer

It is always inconsistent.

Question 28

What is the definition of a matrix?

Accepted Answer

A rectangular array of numbers or variables arranged in rows and columns

Answer

A graph with points plotted on it

Answer

A function that maps one set to another

Answer

A set of ordered pairs

Question 29

Determine the order of a matrix with 4 rows and 5 columns.

Accepted Answer

4 x 5

Answer

5 - 4

Answer

4 + 5

Answer

5 x 4

Question 30

What is the identity matrix?

Accepted Answer

A square matrix with 1s on the diagonal and 0s everywhere else

Answer

A matrix with all elements equal to 1

Answer

A matrix with all elements equal to 0

Question 31

Define the inverse of a matrix.

Accepted Answer

A matrix that, when multiplied by the original matrix, results in the identity matrix

Answer

A matrix that is equal to the original matrix

Answer

A matrix that, when multiplied by the original matrix, results in a zero matrix

Question 32

Identify a common application of matrices.

Accepted Answer

Representing systems of linear equations

Answer

Calculating the volume of a sphere

Answer

Solving quadratic equations

Answer

Finding the area of a triangle

Question 33

What is a determinant of a matrix?

Accepted Answer

A numerical value associated with a square matrix

Answer

The sum of the elements of a matrix

Answer

A row or column of a matrix

Answer

The product of the elements of a matrix

Question 34

State a property of determinants.

Accepted Answer

The determinant of the transpose of a matrix equals the determinant of the original matrix

Answer

The determinant of a matrix is always negative

Answer

The determinant of a matrix is always positive

Question 35

What is Cramer's rule?

Accepted Answer

A method for solving systems of linear equations using determinants

Answer

A method for calculating the determinant of a matrix

Answer

A method for finding the inverse of a matrix

Question 36

Which of the following best describes a matrix?

Accepted Answer

A rectangular arrangement of numbers in rows and columns

Answer

A set of numbers in any order

Answer

A line in a plane

Answer

A function that maps one set of numbers to another

Question 37

Determine the order of the matrix: [1 2 3; 4 5 6; 7 8 9]

Accepted Answer

3 x 3

Answer

2 x 3

Answer

3 x 2

Question 38

Find the sum of the matrices: [1 2; 3 4] and [5 6; 7 8]

Accepted Answer

[6 8; 10 12]

Answer

[2 4; 6 8]

Answer

[8 10; 12 14]

Answer

[4 6; 8 10]

Question 39

Find the rank of the matrix: [1 2 3; 4 5 6; 7 8 9]

Accepted Answer

3

Answer

0

Answer

2

Answer

1

Question 40

What is the defining characteristic of a diagonal matrix?

Accepted Answer

A square matrix with non-zero entries only on the main diagonal

Answer

A rectangular matrix with all entries equal to 0

Answer

A square matrix with all entries equal to 1

Question 41

Which of the given matrices has a multiplicative inverse?

Accepted Answer

[2 1; -1 2]

Answer

[1 2; 3 4]

Answer

[0 1; 0 0]

Question 42

Which of the matrices is an identity matrix?

Accepted Answer

[1 0; 0 1]

Answer

[2 0; 0 2]

Answer

[1 2; 3 4]

Answer

[0 1; 1 0]

Question 43

Identify the diagonal matrix from the following options.

Accepted Answer

[2 0 0; 0 3 0; 0 0 4]

Answer

[2 1 0; 0 3 1; 0 0 4]

Answer

[0 1 0; 1 0 1; 0 1 0]

Answer

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

Question 44

Which of the following matrices represents the identity matrix?

Accepted Answer

[1 0] * [0 1]

Answer

[2 0] * [0 2]

Answer

[0 1] * [1 0]

Question 45

Identify an example of a singular matrix.

Accepted Answer

[1 0] * [0 0]

Answer

[0 1] * [1 0]

Answer

[3 -1] * [-1 3]

Answer

[2 1] * [1 2]

Question 46

Which system of equations is represented by the augmented matrix: [ 1 2 | 5 ]
[ 3 4 | 11 ]?

Accepted Answer

x + 2y = 5
3x + 4y = 11

Answer

2x + y = 5
4x + 3y = 11

Answer

x + 3y = 5
2x + 4y = 11

Answer

x + 2y = 11
3x + 4y = 5

Question 47

What is the identity matrix of order 2?

Accepted Answer

[ 1 0 ]
[ 0 1 ]

Answer

[ 0 0 ]
[ 0 0 ]

Answer

[ 0 1 ]
[ 1 0 ]

Answer

[ 1 1 ]
[ 1 1 ]

Question 48

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

Accepted Answer

Square Matrix

Answer

Row Matrix

Answer

Column Matrix

Answer

Diagonal Matrix

Question 49

Which of the following operations is NOT defined for matrices?

Accepted Answer

Division

Answer

Multiplication

Answer

Addition

Answer

Subtraction

Question 50

If a matrix has 'm' rows and 'n' columns, its order is represented as:

Accepted Answer

m x n

Answer

m - n

Answer

m + n

Answer

n x m