Question | Answer |

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

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

when you multiply this with a matrix it is like multiplying by one | |

3-or more-parameter solution = | |

When vectors can be written as linear combinations of each other they are | |

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

0-parameter solution = | |

vector of length one | |

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

a basic solution to a linear program in which all variables are nonnegative | |

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

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

the number of vectors in a basis for a vector space | |

when it costs less then $1 in raw materials to make $1 worth of product | |

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

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

system of linear equations with one or more solutions | |

If det(A) does not equal 0 then A is | |

vector starting at the origin and ending at a point | |

the distance between vector u and the projection of vector u onto vector v | |

A system is consistent if and only if the row rank of the coefficient matrix equals the row rank of the augmented matrix | |

vector v = c1v1+c2v2+...+ckvk for some scalars c1,c2...ck | |

using row operations to put a matrix into ref | |