If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Main content

Unit: Matrices

Not feeling ready for this? Check out Get ready for Precalculus.

0

Possible mastery points

Introduction to matrices

Learn

Using matrices to represent data

Learn

Practice

Use matrices to represent dataGet 3 of 4 questions to level up!

Multiplying matrices by scalars

Learn

Practice

Multiply matrices by scalarsGet 3 of 4 questions to level up!

Adding and subtracting matrices

Learn

Practice

Add & subtract matricesGet 3 of 4 questions to level up!

Properties of matrix addition & scalar multiplication

Learn

Using matrices to manipulate data

Learn

Practice

Use matrices to manipulate dataGet 3 of 4 questions to level up!

Quiz 1

Level up on the above skills and collect up to 320 Mastery points

Matrices as transformations of the plane

Learn

Practice

Understand matrices as transformations of the planeGet 3 of 4 questions to level up!

Using matrices to transform the plane

Learn

Practice

Use matrices to transform the planeGet 3 of 4 questions to level up!

Transforming 3D and 4D vectors with matrices

Learn

Practice

Use matrices to transform 3D and 4D vectorsGet 3 of 4 questions to level up!

Multiplying matrices by matrices

Learn

Practice

Multiply matricesGet 3 of 4 questions to level up!

Properties of matrix multiplication

Learn

Quiz 2

Level up on the above skills and collect up to 320 Mastery points

Representing systems of equations with matrices

Learn

Practice

Use matrices to represent systems of equationsGet 3 of 4 questions to level up!

Introduction to matrix inverses

Learn

Practice

Determine invertible matricesGet 3 of 4 questions to level up!

Finding inverses of 2x2 matrices

Learn

Finding inverses of 2x2 matrices
(Opens a modal)

Practice

Find the inverse of a 2x2 matrixGet 3 of 4 questions to level up!

Solving linear systems with matrices

Learn

Practice

Use matrices to solve systems of equationsGet 3 of 4 questions to level up!

Quiz 3

Level up on the above skills and collect up to 320 Mastery points

Up next for you:

Unit test

Level up on all the skills in this unit and collect up to 1200 Mastery points!

About this unit

Learn what matrices are and about their various uses: solving systems of equations, transforming shapes and vectors, and representing real-world situations. Learn how to add, subtract, and multiply matrices, and find the inverses of matrices.