NEW
Font size
WorksheetsMatrix Quiz Week 2 I - CSC C
Total questions: 10
Worksheet time: 5mins
If A is a square matrix, which of the following statements is true about its eigenvalues?
They can be complex numbers
They are always real numbers
They are always positive
They must all be distinct.
For a given n×n matrix A , how many eigenvalues can it have at most?
n-1
n
2n-1
Ifinity
If λ is an eigenvalue of the matrix A, which of the following statements is true?
λ is the sum of the eigenvalues of A.
The eigenvectors corresponding to λ are always orthogonal.
λ is a solution to the characteristic polynomial of A.
λ must be an integer
If a matrix A is diagonalizable, which of the following is necessarily true?
All eigenvalues are distinct
The matrix is symmetric
It has a complete set of linearly independent eigenvectors
It has at least one positive eigenvalue
The sum of the eigenvalues of a matrix A is equal to:
The trace of A
The determinant of A
The product of the eigenvalues.
The inverse of the matrix
Which of the following matrices does NOT have real eigenvalues?
A symmetric matrix.
A skew-symmetric matrix
A Hermitian matrix
A real diagonal matrix
If A is a 2×2 matrix with eigenvalues λ1 and λ2, what is the product of the eigenvalues equal to?
The sum of the eigenvalues
The determinant of A
The trace of A
The inverse of the matrix
If a matrix A has an eigenvalue λ=0, what can be said about the matrix?
A is invertible
The determinant of A is zero
All eigenvalues are zero
The matrix is symmetric
For a matrix AAA, if λ\lambdaλ is an eigenvalue with a multiplicity kkk, which of the following statements is true?
The algebraic multiplicity of λ is k
The geometric multiplicity of λ is k
A must have k distinct eigenvectors corresponding to λ
None of the above
Which of the following properties holds for eigenvectors corresponding to distinct eigenvalues of a matrix A?
They are always linearly dependent
They are always orthogonal if A is symmetric
They cannot form a basis
They are unique
