MAT224 Assignment 5 Solutions
1. (a) Let A be a symmetric 2 2 matrix with positive eigenvalues. Show that
x, y = xt Ay,
2 1
, then
1 1
denes an inner product on R2 . (For instance, if A =
1
0
,
1
1
2
MAT224 Assignment 4 Solutions
1. Let V is an n-dimensional vector space, and , , are three bases of V. Let I : V V be the identity
map. Let A = [I] and B = [I] .
(a) Express [I] , [I] , [I] and [I] in
MAT224 Assignment 2 - SOLUTIONS
Due Tuesday Oct 13 at the beginning of the lecture
1. In each part, a linear map (also called a linear transformation) between two vector spaces is given, together with
MAT224 Assignment 2
Due Tuesday Oct 13 at the beginning of the lecture
Attention: Please write your arguments carefully. Neatness will count. Marks may be taken off if your
arguments are not clear or
MAT224 Assignment 3 Solutions
1. Exercise #8 of 2.5. (You should use Proposition 2.5.13 for Part (b).)
Solution: (a) Calculating D(xn ) for 0 n 4 and Int(xn ) for 0 n 3 we get
0 1 0 0 0
0 0 2 0 0
[D]