This is a matrix A in Mathematica format {{2, -1, 0}, {-1, 3, -1}, {0, -1, 4}}. Is the vector b= {{1},{-1},{-1}} an eigenvector of this matrix? If it is not enter “no”. Otherwise, enter the corresponding eigenvalue. Happy for you to use Mathematica.

Let A be a matrix that has an eigenvector. What is the minimum total number of eigenvectors of such a matrix: 0, 1, 2, or infinity?

Let A be a 3x3 matrix. Then A0 = 30, with 0 being the zero vector of the appropriate size. Therefore 0 is an eigenvector of A with eigenvalue 3. True or false?

A matrix A can be diagonalised and one diagonal matrix D corresponding to it is this one

That's correct :) The matrix A can be diagonalised and one diagonal matrix D corresponding to it is this one

Which of the following statements are true?  Select all that apply.

Can the following matrix be diagonalised?

Let's say A is a 3x3 matrix that has the three eigenvalues 0.1, 0.2, and 0.3 and can be diagonalised. Let v be an arbitrary vector in R³. Then the limit of Aⁿv as n goes to infinity is the vector w. What is the sum of the entries of w.