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# AR Linear Algebra

### Linear Algebra

Question | Answer |
---|---|

linear equation | An equation that can be qritten in the form a1x1 + a2x2 + ... + anxn = b, where b and the coeffiecients a1,...,an are real or complex numbers |

augmented matrix | a matrix made up of a coefficient matrix for a linear system and one or more columns to the right. |

linear system | A collection of one or more linear equations involving the same variables, say x1,...,xn |

solution | a list of numbers that makes each equation in the system a true statement when the values s1...sn are substituted for x1,...xn |

solution set | the set of all possible solutions of a linear system. The solution set is empty when the linear system is inconsistent |

equivalent systems | linear systems with the same solution set |

basic variable | a variable in a linear system that corresponds to a pivot column in the coefficient matrix |

free variable | any variable in a linear system that is not a basic variable |

full rank matrix | an m x n matrix whose rank is the smaller of m and n |

kernel | the set of x in V such that T(x)=0 |

Created by:
aelkins