Provide definitions for the following a Define what it means

Provide definitions for the following:

(a) Define what it means for a set B to be a basis for a vector space V.

(b) Define what the dimension of a vector spce is.

Solution

(a) The basis of a vector space V , is the set B of the vector which span vector space V or spanning set of V and also this set B of vectors is linearly independent . In other words , every element of V can be written as linear combination of this set B .

(b) The total number of elements present in basis of vector space V , is known as dimension of vector space V