##### Reference no: EM131023263

Question 1

Consider the vectors

a = (0, 3, -2, 1, 4); b = (5, 2, 1, 0, -1); c = (7, -3, 6, 21, 0)

(a) Find the length of the vector v = 2a - b;

(b) Are are of the given three vectors parallel or orthogonal? Indicate which (if any).

Question 2

Show that the vectors (1, 2, -1, 4), (0, 1, 0 , -1), (1, 3, -1, 1), (-2, -4, 2, -1) are linearly dependent.

Question 3

Find all eigenvalues and eigenvectors of the matrix

A = [5 8/3 -2/3; 2 2/3 4/3; -4 -4/3 -8/3]

Show your work.

Question 4

Write a paragraph answering each of the following questions.

(a) In solving a typical eigenvalue problem, what is given and what is sought?

(b) What is diagonalisation of a matrix? Describe how diagonalisation helps to solve systems of linear differential equations.