Problems Prove Theorem 4.5.2 . Theorem 4.5.2 .Let { v 1 , v 2 , ... , v k } be a set of at least two vectors in a vector space V . If one of the vectors in the set is a linear combination of the other vectors in the set, then that vector can be deleted from the given set of vectors and the linear span of the resulting set of vectors will be the same as the linear span of { v 1 , v 2 , ... , v k } .
Problems Prove Theorem 4.5.2 . Theorem 4.5.2 .Let { v 1 , v 2 , ... , v k } be a set of at least two vectors in a vector space V . If one of the vectors in the set is a linear combination of the other vectors in the set, then that vector can be deleted from the given set of vectors and the linear span of the resulting set of vectors will be the same as the linear span of { v 1 , v 2 , ... , v k } .
Solution Summary: The author explains the theorem mathrm4.5.2 and calculates the linear span of the set of vectors.
Theorem
4.5.2
.Let
{
v
1
,
v
2
,
...
,
v
k
}
be a set of at least two vectors in a vector space
V
. If one of the vectors in the set is a linear combination of the other vectors in the set, then that vector can be deleted from the given set of vectors and the linear span of the resulting set of vectors will be the same as the linear span of
{
v
1
,
v
2
,
...
,
v
k
}
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY