Given that ,
be a set of three dimensional vector in .
Since , is a Vector space over then
Again we known that , If is a Vector Space of finite dimension n .Then 1) Any linearly independent set
with n elements is a basis of V.
2) Any spanning set of with n elements is a basis of .
Since cardinality of is 3 ,Hence by (1) , is a basis of and if the set spanning by (2) , is a basis of .
Comments
Leave a comment