Linear Algebra made completely easy!

We've got you covered—master 45 different topics, practice over 70 real world examples, and learn all the best tips and tricks.

Get Started Now
  • Meet Billy, your Linear Algebra tutor
  • Watch how we take you through a lesson
  • Learn how to find and search for topics
Customer Reviews
4.5 stars based on 2 reviews.

Linear Algebra topics

1Linear Equations with Matrices

1.1Notation of matrices
1.2Solving systems of linear equations by graphing
1.3Representing linear system as a matrix
1.4The three types of matrix row operations
1.5Solving a linear system with matrices using Gaussian elimination
1.6Row reduction and echelon forms
1.7Linear combination and vector equations in RnR^n
1.8Matrix equation Ax=b
1.9Solution sets of linear systems
1.10Application of linear systems

2Linear Transformation

2.1Linear independence
2.2Image and range of linear transformations
2.3Properties of linear transformation
2.4The matrix of a linear transformation

3Matrix Operations

3.1Adding and subtracting matrices
3.2Multiplying a matrix by a scalar
3.3Multiplying a matrix by another matrix
3.4Zero matrix
3.5Identity matrix
3.6Properties of matrix addition
3.7Properties of matrix scalar multiplication
3.8Properties of matrix to matrix multiplication

4Determinant of a Matrix

4.1The determinant of a 2 x 2 matrix
4.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
4.3Properties of determinants
4.4Solving linear systems using Cramer's Rule

5Inverse of Matrices

5.12 x 2 invertible matrix
5.2The inverse of a 2 x 2 matrix
5.3Solving linear systems using 2 x 2 inverse matrices
5.4The inverse of a 3 x 3 matrices with matrix row operations
5.5The invertible matrix theorem

6Subspace of Rn\Bbb{R}^n

6.1Properties of subspace
6.2Column space
6.3Null space
6.4Dimension and rank

7Eigenvalue and Eigenvectors

7.1Eigenvalues and eigenvectors
7.2The characteristic equation
7.3Diagonalization
7.4Complex eigenvalues
7.5Discrete dynamical systems

8Orthogonality and Least Squares

8.1Inner product, length, and orthogonality
8.2Orthogonal sets
8.3Orthogonal projections
8.4Least-squares problem
8.5Applications to linear models
Don't see what you need?
Don't fret, try searching all of our topics
Students and parents love our maths help
But don't take our word for it…
Carson E.
parent

When we saw our son's grades we looked online for a convenient, affordable and effective solution. StudyPug has been a great investment.

Jason G.
high school senior

This website saved my butt last semester. I am using it againthis semester. Dennis is the best online tutor... I also like that I can watch videos over and over until I really understand the concept. If you want to save time, sign up...it's only ten bucks and it saved me hours of study time. Thanks, Dennis!

Aaron M.
high school student

I get a whole library of videos that covers everything from basic to complex mathematics for a very low monthly price. Excellent videos, easy-to-understand and most of all they work. My math test results are 10 points higher than last semester.

See all our Testimonials

Ready to do better in Linear Algebra?

Don't procrastinate any longer, it could be too late!

  • Popular
  • Primary
  • Secondary
  • University
  • All courses