Sincetransgalactic said:V is a vector space on field F and there is a series[tex]v=(v_1,v_2,v_3,v_4)[/tex]
which is independent on V
W_1=sp(v1,v2)
W_2=sp(v2,v3)
of V
prove that
[tex]
W_1\cap W_2=sp(v2)
[/tex]
its obvious v2 exists in both groups .
how am i supposed to prove it
??
A subspace is a subset of a vector space that satisfies all the properties of a vector space. It is closed under addition and scalar multiplication, and contains the zero vector.
To prove that a set is a subspace, you must show that it satisfies the three properties of a vector space: closure under addition, closure under scalar multiplication, and contains the zero vector. This can be done by showing that the set contains all possible linear combinations of its elements and that it contains the zero vector.
A proof by contradiction is a type of mathematical proof that involves assuming the opposite of what you are trying to prove and showing that it leads to a contradiction. This means that the original assumption must be false, and therefore the statement being proved is true.
A subspace is a subset of a vector space that satisfies all the properties of a vector space, while a span is the set of all possible linear combinations of a given set of vectors. In other words, the span of a set of vectors is a subspace if and only if the set of vectors itself is a subspace.
Subspace proofs are used in various fields such as physics, engineering, and computer science to analyze and solve problems involving vector spaces, such as motion, forces, and data analysis. They can also be used to prove the validity of mathematical models and theories.