Solution of Assignment # 3 (Lecture# 21 - 30) Of MTH501 (Spring
2012)
Maximum Marks: 20
Due Date: June 18, 2012
Question: 1 Marks: 10
Find a standard basis vector that can be added to the set {v1, v2} to produce a basis for R3 where;
v1 = (-1, 2, 3), v2 = (1, -2, -2)
Solution:
Any vector not in the plane of given vectors 1
vand 2
vcould be from the third vector of the basis.
The vector perpendicular to both the given vectors will be in another plane, so it could be the third
vector of the basis.
So such vector could be
3
12 3
122
( 4 6) (2 3) (2 2)
20
2
,
(2,1,0).
ijk
ijk
ij k
ij
So
the third vecto r is v
Question: 2 Marks: 10
Let B = {b1, b2} and C = {c1, c2} be the bases for R2. Find the change-of-coordinates matrix from B
to C, and change-of-coordinates matrix from C to B where;
1111
,,,
8541
1212
bbcc
Solution:
The change of coordinate matrix BC
P
is computed by
docsity.com
