hw-sco_109_linearalgebra_i_1.docLINEAR ALGEBRA FOR COMPUTER SCIENCE CAT II
a) Determine whether u=(2,8,2) is a linear combination of u1=(2,-2,0). u2=(3,0,3) and u3=(-2,0,-1)
a. or not (5 marks)
b) Show that the set of vectors
k
j
a
2
-
=
r
,k
j
i
a
+
-
=
r
andk
j
i
c
+
+
=
2
r
is linearly independent (6 marks)c) What do you understand by the phrase “u is a linear combination of u1, u2,u3,…un” (3 marks)
d) Determine whether the vector is a linear combination of the vectors
and
(5 marks)
e) Consider the set B= {(1,1,1), (0,2,2), (0,0,3)}, show that B
i. Spans R3 (3 marks)
ii. is linearly independent (3 marks)
