Matrix Math: Conquer Matrices with Interactive Quizzes

Question 1

Which of the following is NOT a valid matrix operation?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 2

Given matrices A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], calculate A + B.

Accepted Answer

[[6, 8], [10, 12]]

Answer

[[1, 2], [10, 12]]

Answer

[[6, 8], [3, 4]]

Answer

Addition is not defined for matrices of different sizes

Question 3

Which of the following operations cannot be performed on matrices?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 4

Which of the following matrices is the inverse of the matrix [[1, 2], [3, 4]]?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 5

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

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 6

Which of the following operations is not applicable to matrices?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 7

Calculate the product of the matrices [[1, 0], [2, 1]] and [[3, 4], [5, 6]].

Accepted Answer

[[3, 4], [11, 14]]

Answer

[[1, 2], [5, 7]]

Answer

[[3, 4], [5, 6]]

Answer

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

Question 8

Which of the following is NOT a property of matrices?

Accepted Answer

Commutative property for multiplication

Answer

Associative property for addition

Answer

Distributive property for addition

Answer

Existence of an additive identity matrix

Question 9

The inverse of a matrix A, denoted as A^-1, satisfies which of the following equations?

Accepted Answer

AA^-1 = A^-1A = I

Answer

AA^-1 = 0

Answer

A^-1A = 0

Answer

AA^-1 = A

Question 10

Which of the following is the transpose of the matrix A = [1 2; 3 4]?

Accepted Answer

[1 3; 2 4]

Answer

[1 2; 3 4]

Answer

[4 2; 3 1]

Answer

[2 1; 4 3]

Question 11

What is the determinant of the matrix A = [2 1; 3 4]?

Accepted Answer

5

Answer

-5

Answer

1

Answer

-1

Question 12

Which of the following is a singular matrix?

Accepted Answer

[0 1; 0 0]

Answer

[1 2; 3 4]

Answer

[2 3; 4 5]

Answer

[1 2; 2 4]

Question 13

What is the cofactor of the element a_23 in the matrix A = [1 2 3; 4 5 6; 7 8 9]?

Accepted Answer

-7

Answer

7

Answer

1

Answer

-1

Question 14

Which of the following is NOT a typical application of matrices?

Accepted Answer

Creating artistic patterns

Answer

Solving systems of linear equations

Answer

Computer graphics

Answer

Analyzing economic data

Question 15

Which of the following is the transpose of the matrix D = [[1, 2, 3], [4, 5, 6]]?

Accepted Answer

[[4, 1], [5, 2], [6, 3]]

Answer

[[1, 2, 3], [4, 5, 6]]

Answer

[[3, 2, 1], [6, 5, 4]]

Answer

[[1, 4], [2, 5], [3, 6]]

Question 16

If the matrix E = [[a, b], [c, d]] has a determinant of 0, what can you conclude?

Accepted Answer

The matrix is singular.

Answer

The matrix is invertible.

Answer

The matrix is square.

Answer

The matrix has no eigenvalues.

Question 17

What is the order of the matrix F = [[1, 2, 3], [4, 5], [6, 7]]?

Accepted Answer

2x3

Answer

3x2

Answer

3x3

Answer

2x2

Question 18

Which of the following matrices is symmetric?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 19

What is the rank of the matrix G = [[1, 2], [3, 6]]?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 20

Which method is NOT used to find the inverse of a square matrix?

Accepted Answer

Cramer's rule

Answer

Adjoint method

Answer

Row reduction

Answer

Determinant method

Question 21

Which operation is **not** valid for matrices?

Accepted Answer

Exponentiation

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 22

Given matrices A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], calculate A + B.

Accepted Answer

[[6, 8], [10, 12]]

Answer

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

Answer

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

Answer

[[1, 2], [5, 6]]

Question 23

Find the multiplicative inverse of the matrix [[2, 3], [4, 5]].

Accepted Answer

[[-5, 3], [4, -2]]

Answer

[[-5, -3], [4, 2]]

Answer

[[-2, -3], [5, 4]]

Answer

This matrix does not have an inverse.

Question 24

Given the matrix A = [[1, 0], [0, 1]], calculate A^2.

Accepted Answer

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

Answer

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

Answer

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

Answer

This matrix cannot be raised to the power of 2.

Question 25

Find the determinant of the matrix [[a, b], [c, d]] using the cofactor expansion method.

Accepted Answer

ad - bc

Answer

a - b + c - d

Answer

a/b + c/d

Question 26

Which of the following matrices is singular?

Accepted Answer

0 1
                   0 0

Answer

1 2
                   3 4

Answer

2 1
                   -1 2

Question 27

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

Accepted Answer

Commutative

Answer

Distributive over matrix addition

Answer

Associative

Question 28

Find the inverse of the matrix [[3, 2], [1, 1]]

Accepted Answer

[[1/5, -2/5], [-1/5, 3/5]]

Answer

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

Answer

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

Answer

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

Question 29

Find the product of the matrices [[2, 1, 0], [0, 2, 1], [1, 0, 2]] and [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

Accepted Answer

[[14, 20, 26], [4, 11, 18], [19, 26, 33]]

Answer

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

Answer

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

Answer

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

Question 30

Which of the following is a special type of matrix with all elements below the main diagonal being zero?

Accepted Answer

Lower triangular matrix

Answer

Identity matrix

Answer

Diagonal matrix

Answer

Upper triangular matrix

Question 31

To multiply matrices A and B, multiply corresponding elements and add the results. Calculate the product of A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]] using this method.

Accepted Answer

[[11, 14], [31, 38]]

Answer

[[5, 10], [15, 20]]

Answer

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

Question 32

How do you add two matrices?

Accepted Answer

Add the corresponding elements in each matrix.

Answer

Find the determinant of each matrix and add them.

Answer

Multiply the corresponding elements in each matrix and add the products.

Answer

Subtract the corresponding elements in each matrix.

Question 33

What is the result of multiplying a matrix by its transpose?

Accepted Answer

A symmetric matrix

Answer

A skew-symmetric matrix

Answer

A singular matrix

Answer

An invertible matrix

Question 34

Which operation is not defined for matrices?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 35

What is the determinant of a 2x2 matrix?

Accepted Answer

ad - bc

Answer

a - d

Answer

a + d

Question 36

Which matrices have inverses?

Accepted Answer

Matrices with a non-zero determinant

Answer

Matrices with a zero determinant

Answer

Square matrices

Answer

Rectangular matrices

Question 37

What is the inverse of a diagonal matrix?

Accepted Answer

A diagonal matrix with the reciprocals of the diagonal elements.

Answer

A triangular matrix.

Answer

A diagonal matrix with the same diagonal elements.

Question 38

Which application of matrices is commonly used in computer graphics?

Accepted Answer

Transformations

Answer

Finding the area of a triangle

Answer

Calculating eigenvalues and eigenvectors

Answer

Solving systems of equations

Question 39

What is the rank of a matrix?

Accepted Answer

The number of linearly independent rows or columns.

Answer

The number of rows in the matrix.

Answer

The number of columns in the matrix.

Question 40

Which property is unique to orthogonal matrices?

Accepted Answer

Their inverse is equal to their transpose.

Answer

Their determinant is equal to 1.

Answer

Their columns are linearly independent.

Answer

Their eigenvalues are all real.

Question 41

What is the trace of a matrix?

Accepted Answer

The sum of its diagonal elements.

Answer

The number of its distinct eigenvalues.

Answer

The determinant of its diagonal elements.

Answer

The product of its diagonal elements.

Question 42

Which operation cannot be performed on matrices?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 43

Which operation is not applicable to matrices?

Accepted Answer

Division

Answer

Multiplication

Answer

Addition

Answer

Subtraction

Question 44

Determine the inverse of the matrix: [2 3] [-1 2]

Accepted Answer

[0.4 -0.6] [0.2 0.8]

Answer

[0.6 0.4] [0.8 -0.2]

Answer

[-0.4 0.6] [-0.8 0.2]

Answer

[0.6 -0.4] [0.8 0.2]

Question 45

Which matrix is an example of a diagonal matrix?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 46

Given the matrices A = [ [1, 2], [3, 4] ] and B = [ [5, 6], [7, 8] ], compute the result of A + B.

Accepted Answer

[[6, 8], [10, 12]]

Answer

[[5, 6], [1, 2]]

Answer

[[1, 2], [5, 6]]

Answer

[[10, 12], [6, 8]]

Question 47

Calculate the determinant of the matrix C = [ [2, 1], [-3, 4] ].

Accepted Answer

11

Answer

5

Answer

-5

Answer

-11

Question 48

Consider the matrix E = [ [1, 0], [0, 1] ]. Find the result of E^2.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 49

In a system of linear equations, it can be represented as a matrix equation AX = B, where A is the matrix of coefficients, X is the column matrix of unknowns, and B is the column matrix of constants. If A is a square and invertible matrix, how do you solve for X?

Accepted Answer

X = A^−1B

Answer

X = B − A

Answer

X = BA^−1

Answer

X = A + B

Question 50

Which of the following transformations can be expressed using a matrix?

Accepted Answer

Rotation, translation, and scaling

Answer

Addition and subtraction

Answer

Multiplication and division

Answer

Logarithms and exponentials

Question 51

A matrix is considered singular if its determinant is:

Accepted Answer

Zero

Answer

One

Answer

Positive

Answer

Negative

Question 52

The rank of a matrix is equal to the number of:

Accepted Answer

Linearly independent rows or columns

Answer

Elements in the matrix

Answer

Columns in the matrix

Answer

Rows in the matrix