# Matrices

This topic covers: - Adding & subtracting matrices - Multiplying matrices by scalars - Multiplying matrices - Representing & solving linear systems with matrices - Matrix inverses - Matrix determinants - Matrices as transformations - Matrices applications

This course contains 17 segments:

**Introduction to matrices**

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

**Representing linear systems of equations with augmented matrices**

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

**Elementary matrix row operations**

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

**Row-echelon form & Gaussian elimination**

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

**Adding & subtracting matrices**

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

**Multiplying matrices by scalars**

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.

**Properties of matrix addition & scalar multiplication**

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

**Multiplying matrices by matrices**

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

**Properties of matrix multiplication**

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!).

**Matrices as transformations**

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

**Determinant of a 2x2 matrix**

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

**Introduction to matrix inverses**

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

**Finding the inverse of a matrix using its determinant**

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

**Practice finding the inverses of 2x2 matrices**

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

**Determinants & inverses of large matrices**

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

**Solving equations with inverse matrices**

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

**Model real-world situations with matrices**

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

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Rating | Not enough ratings |
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Length | 17 segments |

Starts | On Demand (Start anytime) |

Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math |

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Rating | Not enough ratings |
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Length | 17 segments |

Starts | On Demand (Start anytime) |

Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math |

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