FREE
Linear Algebra Practice Tests

varsity tutors app store varsity tutors android store

Free Linear Algebra Diagnostic Tests

Take the Varsity Learning Tools free diagnostic test for Linear Algebra to determine which academic concepts you understand and which ones require your ongoing attention. Each Linear Algebra problem is tagged down to the core, underlying concept that is being tested. The Linear Algebra diagnostic test results highlight how you performed on each area of the test. You can then utilize the results to create a personalized study plan that is based on your particular area of need.

Linear Algebra Diagnostic Test 1

Questions: 20
Test Difficulty:
Average Time Spent: 4 mins

Linear Algebra Diagnostic Test 2

Questions: 20
Test Difficulty:
Average Time Spent: 2 hrs 0 mins

Linear Algebra Diagnostic Test 3

Questions: 12
Test Difficulty:
Average Time Spent: 5 mins

Linear Algebra Diagnostic Test 4

Questions: 12
Test Difficulty:
Average Time Spent: 7 mins

Free Linear Algebra Practice Tests

Our completely free Linear Algebra practice tests are the perfect way to brush up your skills. Take one of our many Linear Algebra practice tests for a run-through of commonly asked questions. You will receive incredibly detailed scoring results at the end of your Linear Algebra practice test to help you identify your strengths and weaknesses. Pick one of our Linear Algebra practice tests now and begin!

The free Linear Algebra Practice Tests offered within the comprehensive Varsity Tutors’ Learning Tools offers powerful assessment capabilities for students who wish to discover their academic strengths and to pinpoint the concepts they need to focus their studies on. All the essential concepts are covered in the study materials, including linear equations, matrices, operations and properties, matrix calculus, and many more.

Start your study session by taking a Full-Length Linear Algebra Practice Test. The test consists of 40 questions covering all of the essential concepts of linear algebra. At the end of the test, you will receive in-depth feedback that highlights areas you are already competent in and alerts you to any areas in which you need to polish your skills. In addition to your score, you will see a comparison of how you rank among previous test-takers. The answer to every question, even those you answered correctly, illustrates the step-by-step process of solving the problem as well as a written explanation of how to complete the steps. This valuable knowledge can help you understand the necessary steps in reaching the correct solution. Each question also has links to the relevant concepts so that you can dive deeper into your linear algebra review.

After reviewing your assessment results, you can then utilize the other Learning Tools to create a well-rounded linear algebra study plan. The Learn by Concept Learning Tool provides an interactive syllabus that breaks down each concept by topic so that you can focus on the areas you need to review. You can access a variety of linear algebra example problems that lay out the information you need to learn to solve them for yourself. Hundreds of linear algebra flashcards are organized by concept to allow you to study the concepts that you choose. You can also build your own custom flashcard set with the flashcard creator. The Linear Algebra Question of the Day picks a random question each day from the linear algebra study materials to allow you to quickly review that day’s concept.

Once you have polished your linear algebra skills with Varsity Tutors’ Learning Tools, return to the practice tests and choose from one of several Linear Algebra Practice Tests. These shorter tests consist of a handful of questions to quickly assess your skills on a single concept. You will receive the same detailed feedback from these tests as you did on the Full-Length Practice Tests. Upon reviewing the feedback, you will be able to determine if you are prepared to move forward in your study plan or if you need further review of the concept. Varsity Tutors’ Learning Tools also allow you to build your own practice tests to really sharpen your skills. All the tests are sharable on social media, which means that you can compete with your friends and classmates or study virtually with your study group.

All of Varsity Tutors’ Linear Algebra Learning Tools work together to create a customized study plan to enhance your learning experience. The ability to quickly assess your skills and the flexibility to choose only the topics you need to review means that you will spend less time studying material that you already know and more time focusing on building your linear algebra knowledge.

Practice Tests by Concept

Linear equations practice test

Questions: 40
Test Difficulty:
Average Time Spent: 4 mins

Criteria for uniqueness and consistency practice test

Questions: 12
Test Difficulty:

Homogeneus cases practice test

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 40 secs

Non-homogeneous cases practice test

Questions: 12
Test Difficulty:

Reduced row echelon form and row operations practice test

Questions: 15
Test Difficulty:
Average Time Spent: 4 mins

Row operations and equivalent systems practice test

Questions: 12
Test Difficulty:
Average Time Spent: 2 mins 17 secs

Matrices practice test

Questions: 2
Test Difficulty:

Matrix-matrix product practice test

Questions: 12
Test Difficulty:
Average Time Spent: 3 mins

Matrix-vector product practice test

Questions: 19
Test Difficulty:

Vector-vector product practice test

Questions: 2
Test Difficulty:

Matrix calculus practice test

Questions: 1
Test Difficulty:

Eigenvalues as optimization practice test

Questions: 2
Test Difficulty:
Average Time Spent: 22 secs

Gradients and hessians of quadratic and linear functions practice test

Questions: 12
Test Difficulty:

Gradients of the determinant practice test

Questions: 1
Test Difficulty:

Least squares practice test

Questions: 1
Test Difficulty:

The gradient practice test

Questions: 2
Test Difficulty:

The hessian practice test

Questions: 2
Test Difficulty:

Operations and properties practice test

Questions: 9
Test Difficulty:
Average Time Spent: 1 mins 25 secs

Eigenvalues and eigenvectors practice test

Questions: 1
Test Difficulty:
Average Time Spent: 1 mins 48 secs

Eigenvalues and eigenvectors of symmetric matrices practice test

Questions: 1
Test Difficulty:

Linear independence and rank practice test

Questions: 1
Test Difficulty:
Average Time Spent: 11 secs

Linear mapping practice test

Questions: 12
Test Difficulty:

Norms practice test

Questions: 1
Test Difficulty:

Orthogonal matrices practice test

Questions: 1
Test Difficulty:

Quadratic forms and positive semidefinite matrices practice test

Questions: 12
Test Difficulty:

Range and null space of a matrix practice test

Questions: 1
Test Difficulty:

Symmetric matrices practice test

Questions: 13
Test Difficulty:
Average Time Spent: 44 secs

The determinant practice test

Questions: 6
Test Difficulty:

The identity matrix and diagonal matrices practice test

Questions: 9
Test Difficulty:
Average Time Spent: 2 mins 37 secs

The inverse practice test

Questions: 1
Test Difficulty:

The trace practice test

Questions: 2
Test Difficulty:

The transpose practice test

Questions: 1
Test Difficulty:

Practice Quizzes

Linear Algebra Problem Set 77

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 76

Questions: 12
Test Difficulty:
Average Time Spent: 38 secs

Linear Algebra Problem Set 75

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 74

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 73

Questions: 12
Test Difficulty:
Average Time Spent: 3 mins

Linear Algebra Problem Set 72

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 71

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 70

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 69

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 68

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 67

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 66

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 65

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 64

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 63

Questions: 12
Test Difficulty:
Average Time Spent: 3 mins

Linear Algebra Problem Set 62

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 61

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 60

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 59

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 58

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 57

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 36 secs

Linear Algebra Problem Set 56

Questions: 12
Test Difficulty:
Average Time Spent: 17 mins

Linear Algebra Problem Set 55

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 54

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 53

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 31 secs

Linear Algebra Problem Set 52

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 51

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 50

Questions: 12
Test Difficulty:
Average Time Spent: 3 mins

Linear Algebra Problem Set 49

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 48

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 47

Questions: 12
Test Difficulty:
Average Time Spent: 43 secs

Linear Algebra Problem Set 46

Questions: 12
Test Difficulty:
Average Time Spent: 4 mins

Linear Algebra Problem Set 45

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 44

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 43

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 42

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 41

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 40

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 39

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 23 secs

Linear Algebra Problem Set 38

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 37

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 36

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 35

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 11 secs

Linear Algebra Problem Set 34

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 32

Questions: 12
Test Difficulty:
Average Time Spent: 2 mins 58 secs

Linear Algebra Problem Set 31

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 30

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 29

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 28

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 27

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 26

Questions: 12
Test Difficulty:
Average Time Spent: 2 mins 10 secs

Linear Algebra Problem Set 25

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 24

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 23

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 22

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 21

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 20

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 19

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 18

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 17

Questions: 12
Test Difficulty:
Average Time Spent: 33 secs

Linear Algebra Problem Set 16

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 15

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 14

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 13

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 12

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 11

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 10

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 9

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 8

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 7

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 6

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 5

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 4

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 3

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 5 secs

Linear Algebra Problem Set 2

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

Linear Algebra Problem Set 1

Questions: 12
Test Difficulty:
Average Time Spent: 4 mins
Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: