Question | Answer |

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

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

linear system that does not have any solutions | |

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

the square root of (u1)^2+...+ (uk)^k | |

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

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

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

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

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

1-parameter solution = | |

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

Problem of maximizing or minimizing a linear function over a set of constraints | |

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

3-or more-parameter solution = | |

using row operations to put a matrix into ref | |

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

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

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

A^t (switching a matrix's rows and columns) | |

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

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