MTH501-Linear Algebra

QUIZ 2

Lecture 28-32

FALL 2018

due date: 04 Feb., 2019

QUIZ 2

Lecture 28-32

FALL 2018

due date: 04 Feb., 2019

The null-space of a linear transformation T is the set of all vectors v such that T(v)= |

If A is an n x n matrix, then the following statements are equivalent EXCEPT |

If A is triangular matrix then the eigenvalues of A are the entries on the main diagonal of A |

A row interchange ____ the sign of determinant |

The characteristics polynomial of a 3 x 3 identity matrix is ___ if x is the eigen value of the given 3 x 3 identity matrix |

An n x n matrix with n distinct eigen values is ___ |

If λ is an eigen value of a matrix A and x is a corresponding eigenvector, and if k is any positive integer then λ k is an eigenvalue of ___ and x is corresponding eigenvector. |

If 3 is an eigenvalue of A and x is a corresponding eigenvector then what is the eigenvalue of A^2? |

The dominant or principal eigenvector of a matrix is an eigenvector corresponding to the eigenvalue of ___ magnitude (for real numbers, largest absolute value) of that matrix. |

If n x n matrices A and B are similar. then they have the ___ characteristic polynomial. |

If A be n x n matrix, then det(A^T)= |

An n x n matrix A is diagonalizable if and only if A has n linearly ___ eigenvectors |

If A is a m x n matrix and A=A^T which of the following must always be true? |

An n x n matrix with n distinct values is ___ |

The dominant or principal eigenvector of a matrix is an eigenvector corresponding to the eigenvalue of ___ magnitude (for real numbers, largest absolute value) of that matrix |

If n x n matrices A and B are similar, then they have the ___ characteristic polynomial |

Two matrices with the same characteristic polynomial ___ similar |

If x-2 is a factor of the characteristic polynomial of matrix C then an eigenvalue of C is |

If A and B are n x n matrices, then det (AB) = |

A row interchange ___ the sign of the determinant |