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MTH1030 -1035 - Techniques for modelling - S1 2025
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This is a matrix A in Mathematica format {{3, 1, 0, 0, 0}, {1, 3, 0, 0, 0}, {0, 0, 4, 1, 0}, {0, 0, 0, 4, 0}, {0, 0, 0, 0, 4}}.
Is the vector b={{2},{2},{1},{0},{0}}an eigenvector of this matrix? If it is not enter “no”. Otherwise, enter the corresponding eigenvalue. Happy for you to use Mathematica.This matrix
has eigenvalues 1 and 2. If
is an eigenvector corresponding to the eigenvalue 1, what is a?
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
Let a and g be the algebraic and the geometric multiplicities of the eigenvalue 1. What are a and g? Enter your answer in the format a,g.Which of the following statements are true? Select all that apply.
That's correct :) The matrix A can be diagonalised and one diagonal matrix D corresponding to it is this one
How many different eigenvalues does A have?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.