04. Linear Combination -Quiz 1
The following is a set of three vectors:
(1)
(2)
(3)
All three vectors are
SOLUTION:
- (1) and (2)
- (1) and (3)
The question in this quiz may seem a bit strange. We have three vectors, why do they not all define the plane that can be spanned by a linear combination of them all?
A simple glance at vectors and will show you that one vector can be defined as a linear combination of the other.
for example:
In other words, if we use as a part of our linear combination (for creating finding the vectors spanned), we do not need . And vice versa: if we use as a part of our linear combination (for creating finding the vectors spanned), we do not need .
Therefore, to define the plane spanned by a linear combination of the vectors above, we need ( and ) or ( and ).