Recall: Basis Let V be a vector space over a field F. A set of S of vectors in V is snid to be a basis of V if (i) S is linearly independent in V, and
(ii) S generates V ie. linear span of
Theorem: Let V be a vector space of dimension n over a field F. Then any linearly independent set of n vectors of V is a basis of V.
We have to show that 5 is a basis of
Let us consider the relation
Then we have
Fron the above equation we get,
Solving these equation we get,
This proves that the set
Now, we know that
As the dimension of
set containing 4 vectors of
therefore the set
is a basis of
is a basis for
Find an explicit description of Nul A by listing vectors that span the null space.
Assume that A is row equivalent to B. Find bases for Nul A and Col A.