Question | Answer |

the set of all linear combinations of a set of vectors | |

above and below leading ones are zeroes | |

an extra variable that's added to an inequality to make the constraint an equality | |

linear system that does not have any solutions | |

A basis that is also an orthonormal set | |

vector of length one | |

when a linear system has an infinite number of solutions it has: | |

using row operations to put a matrix into ref | |

vector x = vector Po + t times vector v1 + s times vector v2 | |

first nonzero entry in every row is one and below each one are zeroes | |

A vector space W that is part of a larger vector space V | |

a matrix that represents the cost per dollar to run several companies/industries in an economy | |

If given any demand there is a production schedule that meets that demand | |

When no vector in S is a linear combination of the other vectors | |

when one non-zero vector is a scalar multiple of another, these vectors are: | |

2-parameter solution = | |

Vector Sn = T^n times vector So | |

x vector =(x1,x2,...,xn) = Po vector + t times the v vector | |

system where all constraints are 0 (when every equation in the system equals 0) | |

choosing a point in a matrix, turning it into a one, then annihilating entries above and below it | |

3-or more-parameter solution = | |

the number of non-zero rows the matrix has after it has been put in ref | |