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.

Main content

Matrices: FAQ

Frequently asked questions about matrices

What is a matrix?

A matrix is a rectangular array of numbers arranged in rows and columns.
Matrices can be useful for organizing and manipulating data. They can also be used as a tool to help solve systems of equations.

How do we multiply a matrix by a scalar?

To multiply a matrix by a scalar, we multiply each entry in the matrix by the scalar. For example, if
and we want to multiply A by 2, we can multiply each entry by 2 to get:

How do we add or subtract two matrices?

To add or subtract two matrices, we add or subtract corresponding entries. So if

How do we multiply two matrices together?

This one's a bit trickier. To multiply two matrices together, we take the dot product of the rows from the first matrix with the columns from the second matrix. The result is a new matrix. For example, if

What can we do with the inverse of a matrix?

Finding the inverse of a matrix can be useful for solving linear systems of equations. If A is the matrix representing the system of equations, and b is the vector of solutions, then Ax=b. If we can find the inverse of A, we can multiply both sides of the equation by it to isolate x:

Where are matrices used in the real world?

Matrices have tons of real-world applications! They can be used in computer graphics to perform transformations on images, in physics to model physical systems, and in statistics to analyze data, just to name a few.

Want to join the conversation?