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# MTH355 ~ Chp 3 Terms

### Linear Algebra Terms ~ Chp 3, Test 3

Question | Answer |
---|---|

Properties of Determinants: The elements in a row/column of matrix A are multiplied by c. What is B (the resulting matrix)? | B = cA |

Properties of Determinants: Two rows/columns of matrix A are interchanged. What is B (the resulting matrix)? | B = -A |

Properties of Determinants: In matrix A a multiple of one row/column is added to another row/column. What is B (the resulting matrix)? | B = A |

Definition: Determinant of a square matrix | The sum of the products of the elements of a row or column within a matrix and their cofactors. A real number associated with every square matrix. |

Definition: Minor (of an Element) | The minor of element a(ij) is denoted M(ij) and is the determinant of the matrix that remains after deleting row i and column j of matrix A. |

Definition: Cofactor (of an Element) | The cofactor of a(ij) is denoted C(ij) and is given by C(in) = (-1)^(i+j)*M(ij) |

Definition: Determinantal Equation | A determinant that is expanded to yield an equation. |

Definition: Singular Matrix | A square matrix A is said to be singular if A = 0. |

Definition: Nonsingular Matrix | A square matrix A is nonsingular if A /= 0. |

Theorem for Singular Matrices: Let A be a square matrix. A is singular if | 1) All the elements of a row/column are 02) Two rows/columns are equal3) Two rows/columns are proportional |

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sunrise016