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

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 4

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 5

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 6

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 7

Which of the following operations is NOT applicable to matrices?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 8

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 9

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 10

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 11

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 12

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

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 13

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 14

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 15

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 16

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 17

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 18

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 19

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 20

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 21

Name an application of matrices in real life.

Accepted Answer

Computer graphics

Answer

Playing chess

Answer

Baking a cake

Answer

Solving puzzles

Question 22

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 23

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 24

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 25

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 26

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 27

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 28

Which operation is NOT defined for matrices?

Accepted Answer

Division

Answer

Subtraction

Answer

Multiplication

Answer

Addition

Question 29

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 30

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 31

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 32

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 33

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 34

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 35

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 36

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

Accepted Answer

11

Answer

8

Answer

5

Answer

-11

Question 37

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 38

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 39

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 40

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

Accepted Answer

3x5

Answer

5

Answer

5x3

Answer

3

Question 41

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 42

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 43

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]]