Master Matrix Math: Interactive Quizzes and Practice

Question 1

Calculate the determinant of the matrix [[2, 1], [3, 4]]

Accepted Answer

5

Answer

1

Answer

-5

Answer

-1

Question 2

Identify the identity matrix

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 3

Define a diagonal matrix

Accepted Answer

A square matrix with non-zero elements only on its diagonal.

Answer

A square matrix with all elements equal.

Answer

A rectangular matrix with more rows than columns.

Answer

A rectangular matrix with more columns than rows.

Question 4

Calculate the determinant of the matrix [[a, b], [c, d]]

Accepted Answer

a * d - b * c

Answer

a * d + b * c

Answer

c * d - a * b

Answer

c * d + a * b

Question 5

Find the transpose of the matrix [[2, 1, 3], [4, 5, 6]]

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 6

Which of the following matrices is an identity matrix?

Accepted Answer

[1 0; 0 1]

Answer

[0 1; 1 0]

Answer

[2 0; 0 2]

Answer

[-1 0; 0 -1]

Question 7

Which of the following operations is NOT valid for matrices?

Accepted Answer

Dividing one matrix by another

Answer

Adding matrices with matching dimensions

Answer

Multiplying a matrix by a number

Answer

Subtracting matrices with matching dimensions

Question 8

Which of the following operations is NOT applicable to matrices?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 9

Which of the following is a property of an invertible matrix?

Accepted Answer

Determinant is non-zero

Answer

Determinant is zero

Answer

Square matrix

Answer

Symmetric matrix

Question 10

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

Accepted Answer

[1/2, -1/2; -3/8, 1/4]

Answer

[2, -1; -3, 4]

Answer

[1, -2; -3, 4]

Answer

[0, 1; 0, -1]

Question 11

Which of the following is the augmented matrix for the system of equations x + 2y = 3, -x + y = 1?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 12

Which of the following is the null space of the matrix [[1, 2, 3], [4, 5, 6]]?

Accepted Answer

The set of all vectors whose dot product with the matrix is zero

Answer

The set of all vectors parallel to the column space

Answer

The set of all vectors in the row space

Answer

The set of all vectors in the span of the matrix

Question 13

Find the transpose of the matrix [[1, 2], [3, 4], [5, 6]]:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 14

How many columns are in the matrix [[1, 2, 3], [4, 5, 6]]?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 15

Which of the following statements about matrix properties is incorrect?

Accepted Answer

The determinant of a matrix is always negative.

Answer

Matrix addition is commutative.

Answer

Matrix multiplication is associative.

Answer

The identity matrix is a square matrix with 1's on the diagonal.

Question 16

What is the transpose of the matrix [[1, 2], [3, 4], [5, 6]]?

Accepted Answer

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

Answer

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

Answer

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

Answer

The matrix cannot be transposed.

Question 17

What is the order (dimensions) of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?

Accepted Answer

3x3

Answer

2x3

Answer

3x2

Answer

4x3

Question 18

Which of the following matrices is a non-invertible (singular) matrix?

Accepted Answer

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

Answer

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

Answer

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

Answer

[[2, 3], [4, 6]]

Question 19

Which of the following operations is not applicable to matrices?

Accepted Answer

Exponentiation

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 20

Solve the system of equations using matrices: 
 2x + 3y = 7 
 x - y = 1

Accepted Answer

x = 2, y = 1

Answer

x = 1, y = 2

Answer

x = 3, y = 2

Answer

x = 2, y = 3

Question 21

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

Accepted Answer

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

Answer

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

Answer

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

Answer

The matrix does not have an inverse.

Question 22

Which of the following systems of equations can be represented by the matrix equation Ax = b, where A = [[1, 2], [3, 4]], x = [x, y], and b = [5, 10]?

Accepted Answer

x + 2y = 5, 3x + 4y = 10

Answer

x - 2y = 5, 3x + 4y = 10

Answer

x + 2y = 10, 3x + 4y = 5

Answer

x - 2y = 10, 3x + 4y = 5

Question 23

Which of the following transformations can be represented by the matrix [[cos(theta), -sin(theta)], [sin(theta), cos(theta)]]?

Accepted Answer

Rotation

Answer

Translation

Answer

Scaling

Answer

Reflection

Question 24

What is the transpose of the matrix [[1, 2], [3, 4], [5, 6]]?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 25

Which of the following matrices is an identity matrix?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 26

Which of the following is NOT a valid operation for matrices?

Accepted Answer

Addition of a matrix and a vector

Answer

Multiplication of two matrices

Answer

Determinant of a matrix

Answer

Transposition of a matrix

Question 27

Define a null matrix of size 3x2.

Accepted Answer

[0 0; 0 0; 0 0]

Answer

[0 0 0; 0 0 0]

Answer

[1 2; 3 4; 5 6]

Answer

[1 0; 0 1; 0 0]

Question 28

Name an application of matrices in real life.

Accepted Answer

Computer graphics

Answer

Playing chess

Answer

Baking a cake

Answer

Solving puzzles

Question 29

How would you represent the following matrix as a Python list of lists?

[1 2 3]
[4 5 6]

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 30

What is the result of multiplying these two matrices?

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

Accepted Answer

[[19 22]
  [43 50]]

Answer

[[1 2]
  [3 4]]

Answer

[[10 12]
  [21 24]]

Answer

[[5 6]
  [7 8]]

Question 31

Which matrix is the transpose of this one?

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

Accepted Answer

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

Answer

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

Answer

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

Answer

[[1 2]
  [3 4]]

Question 32

What is special about the matrix below?

[[1 0]
  [0 1]]

Accepted Answer

It's the identity matrix.

Answer

It's a diagonal matrix.

Answer

It's a singular matrix.

Answer

It's a symmetric matrix.

Question 33

What is the augmented matrix for this system of equations?

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

Accepted Answer

[[3 -2 | 5]
  [1 1 | 4]]

Answer

[[3 -2 | 4]
  [1 1 | 5]]

Answer

[[3 2 | 5]
  [1 1 | 4]]

Answer

[[1 1 | 4]
  [3 -2 | 5]]

Question 34

Which matrix is row-equivalent to this one after performing elementary row operations?

[[1 2 3]
[0 4 5]
[0 0 6]]

Accepted Answer

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

Answer

[[0 4 5]
  [1 2 3]
  [0 0 6]]

Answer

[[1 2 3]
  [0 5 4]
  [0 6 0]]

Answer

[[3 2 1]
  [5 4 0]
  [6 0 0]]

Question 35

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 36

Which operation is NOT defined for matrices?

Accepted Answer

Division

Answer

Subtraction

Answer

Multiplication

Answer

Addition

Question 37

What is the size of the matrix  [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?

Accepted Answer

3 x 3

Answer

2 x 3

Answer

1 x 9

Answer

3 x 2

Question 38

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 39

Which statement about matrices is NOT true?

Accepted Answer

Matrices can be divided by vectors.

Answer

Matrices can be inverted.

Answer

Matrices can be added and subtracted.

Answer

Matrices can be multiplied by scalars.

Question 40

A matrix has 3 rows and 4 columns. What is its order?

Accepted Answer

3 x 4

Answer

4 x 3

Answer

2 x 3

Answer

3 x 2

Question 41

Which of these is the identity matrix?

Accepted Answer

[1 0; 0 1]

Answer

[0 1; 1 0]

Answer

[1 1; 0 0]

Answer

[0 0; 1 1]

Question 42

What is the order of the matrix  [ 1  2  3 ] ?

Accepted Answer

1 x 3 (1 row and 3 columns)

Answer

3 x 3

Answer

3 x 1

Question 43

Which of the following systems of equations can be represented by the matrix equation [ 2  1 ] [ x ] = [ 5 ]?

Accepted Answer

2x + y = 5

Answer

2x - y = 5

Answer

x - 2y = 5

Answer

x + 2y = 5

Question 44

Which of the following is a valid matrix operation?

Accepted Answer

Addition or subtraction of matrices with the same dimensions

Answer

Multiplication of a matrix by a vector

Answer

Solving a system of equations using a matrix

Question 45

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

Accepted Answer

11

Answer

8

Answer

5

Answer

-11

Question 46

Which of the following systems of equations can be represented by the matrix equation AX = B, where A = [[1, 2], [3, 4]]?

Accepted Answer

x + 2y = 5; 3x + 4y = 12

Answer

x + y = 5; 3x + 2y = 12

Answer

2x + y = 5; 3x + 4y = 10

Question 47

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

Accepted Answer

[[2/7, -3/7], [-1/7, 4/7]]

Answer

[[-2/7, 3/7], [1/7, -4/7]]

Answer

[[1/7, -3/7], [2/7, 4/7]]

Answer

[[-1/7, 3/7], [-2/7, 4/7]]

Question 48

What is the product of the matrices [[1, 2, 3], [4, 5, 6]] and [[7], [8], [9]]?

Accepted Answer

[[58], [104]]

Answer

[[35], [63]]

Answer

[[21], [38]]

Answer

[[29], [52]]

Question 49

Which of the following transformations can be represented by the matrix [[cos(θ), -sin(θ)], [sin(θ), cos(θ)]]?

Accepted Answer

Rotation about the origin by an angle θ

Answer

Reflection across the y-axis

Answer

Translation along the x-axis

Answer

Shear transformation

Question 50

What is the dimension of a matrix that has 3 rows and 5 columns?

Accepted Answer

3x5

Answer

5

Answer

5x3

Answer

3

Question 51

Which of the following is a singular matrix?

Accepted Answer

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

Answer

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

Answer

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

Answer

[[2, -1], [3, 0]]

Question 52

What is the transpose of the matrix [[1, 2, 3], [4, 5, 6]]?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 53

Which of the following matrices is symmetric?

Accepted Answer

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

Answer

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

Answer

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

Answer

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