Question | Answer |

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

vector u times vector v = u1v1+...+unvn | |

using row operations to put a matrix into ref | |

Vector Sn = T^n times vector So | |

linear system that does not have any solutions | |

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

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

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

2-parameter solution = | |

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

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

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

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

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

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

A basis that is also an orthonormal set | |

3-or more-parameter solution = | |

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

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

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

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: | |

vector of length one | |