Math Problem Solver

Problem 1 (10 marks)

A transformation matrix T is shown below:

T =

2 −3

0 5

.

(a) [2 marks] Given a position vector A =

1

1

, explain what happens to A when it undergoes

a transformation under T?

(b) [2 marks] Using eigenvalue decomposition, represent T in terms of eigenvectors matrix,

eigenvalues matrix and inverse eigenvectors matrix.

(c) [1 marks] State the eigenvalues of T.

(d) [1 marks] State the associated eigenvectors of T.

(e) [4 marks] By making a plot, show what happens to the eigenvectors when they undergo a

transformation under T. Include eigenvalues in your interpretation and contrast the result of

this eigenvector transformation with that of position vector A.