Matrices: FAQ

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.

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:

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

and

$B=\left[\begin{array}{cc}5& 2\\ 3& 1\end{array}\right]$‍,

then

and

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

and

$B=\left[\begin{array}{cc}5& 2\\ 3& 1\end{array}\right]$‍,

then

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 $x$‍:

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.