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.
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