## Sunday, 3 February 2019

### MTH501 Linear Algebra Quiz 2 Lecture 28-32 FALL 2018 Due date: 04 Feb, 2019 | SSWT

MTH501-Linear Algebra
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