Question | Answer |

A basis that is also an orthonormal set | |

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

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

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

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

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

method used to find the determinant and/or inverse of a 3x3 matrix or larger | |

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

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

If a set of vectors spans the vector space V and the set is linearly independent it is a | |

If every vector is a unit vector and the vectors are mutually orthogonal then the vectors are | |

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

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

1-parameter solution = | |

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

a matrix where all entries are non-negative and every column sums to one | |

above and below leading ones are zeroes | |

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

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

system of linear equations with one or more solutions | |

2-parameter solution = | |

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

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