basic linear algebra question 1 How to determine Rn Space in

basic linear algebra question!

1. How to determine R^n Space in the matrix? Is that n just the number of columns?

2. How to get rank of matrix?

Any tip for solving linear algebra matrix about vector spaces!

Solution

In vector space, dimension of a vector space is the cardinality or no of vectors of a basis V over its base field.

For every vector space a basis exists the dimension will be the same for all bases.

A basis B of a vector space V is a linearly independent subset of V that spans V.

Suppose B = {v1,v2...vn} for a vector space V

then v1, v2...vn are linearly independent and any vector in V can be written as a linear combination of v1, v2,...vn.

In this case dim = n.

The linear combination of vectors can be represented by a matrix also.

The dimension of vector space = Rank of the matrix.

Rank of a matrix is the no of non zero rows when the matrix is in echelon form (row reduced).