# Matrices

Contents

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.

Learn what matrices are and about their parts (coordinates and dimensions).

Learn how systems of linear equations with multiple variables are represented with matrices.

Learn about the three basic operations we can perform on a matrix without changing the solution set of the linear system it represents.

Learn how to use the matrix row operations in order to easily solve large systems of linear equations.

Learn how to add and subtract two matrices to obtain a new matrix (just like numbers!).

Learn how to multiply matrices by scalars (in the world of matrices, scalars are simply regular numbers). For example, multiply a 2X2 matrix by 3.

Learn about zero matrices and about how matrix addition, subtraction, and scalar multiplication are related to their corresponding operations with real numbers.

Learn how to find the result of a multiplication of two matrices.

Learn about identity matrices and about how matrix multiplication relates to real number multiplication (spoiler: the distributive property applies but the commutative property does not!).

Learn how matrices can be used as transformations of vectors or transformations of the plane.

Learn what the determinant of a matrix is and how to find it for 2x2 matrices.

Learn what the inverse of a matrix is, and how to determine whether two matrices are inverses or whether a matrix is invertible.

Learn about a way to find the inverse of a matrix using its determinant and adjuagates.

After you've learned how to find the inverse of a 2x2 matrix, gain some practice with it.

Learn how to find the determinants and the inverses of matrices with dimensions 3x3 or larger.

Learn how to solve systems of linear equations using inverse matrices, and how to solve matrix equations using inverse matrices.

Learn how matrices can be used to describe real-world situations.