University Examinations 2023/2024 (100% Verified)
LINEAR ALGEBRA II
QUESTION ONE – (30 MARKS)
1 2
a) Given that A and g(t) = - 5t -2, show that A in a root of g(t)
3 4
(4 Marks )
b) Let T: → be defined by show that T is not a linear map.
(4 Marks)
c) Let T be the linear mapping T: defined by T(3,1) = (2,
- 4) and T(1,1) = (0,2). Find
T(x,y). In particular find T(5,7) (4 Marks)
2 3 −4
0 −4 2 =
,compute the minors
and cofactors of each 1 −1 5 element in d) Given the matrix A
column 1. (4 Marks)
e) Let V be the Vector space of polynomials in t of degree, 3 and let D: be the differential
linear mapping defined by = . Find the matrix of D with respect to the
basis 1, , , (5 Marks)
LINEAR ALGEBRA II
QUESTION ONE – (30 MARKS)
1 2
a) Given that A and g(t) = - 5t -2, show that A in a root of g(t)
3 4
(4 Marks )
b) Let T: → be defined by show that T is not a linear map.
(4 Marks)
c) Let T be the linear mapping T: defined by T(3,1) = (2,
- 4) and T(1,1) = (0,2). Find
T(x,y). In particular find T(5,7) (4 Marks)
2 3 −4
0 −4 2 =
,compute the minors
and cofactors of each 1 −1 5 element in d) Given the matrix A
column 1. (4 Marks)
e) Let V be the Vector space of polynomials in t of degree, 3 and let D: be the differential
linear mapping defined by = . Find the matrix of D with respect to the
basis 1, , , (5 Marks)
