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 1
1 1
= 1 1
0
1
= 0.
Suggestion: Note that the 1st requ
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 terms of A and B. (For instance, [I] = A1 .)
(b) Suppo
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 a basis of the domain and a basis of the target. Find
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 if the presentation of your solutions shows a lack of e