Select a basis for Span B given and determine the dimension

Select a basis for Span B (given) and determine the dimension of Span B.

Solution

The dimension of a vector space V is the number of vectors in a basis.

Let V be a vector space and S = {v₁, v₂, ... , v_k} be a subset of V. Then S is a basis for V if the following two statements are true.

So, by both definations assume B ={v₁ ,v₂ , .... V₅}

as V₂ = -2V₁ and 2V₁ + 2V₃ = V₄

SO, Basis of span B ={ V₁ , V₃, V₅ }

Dimension = 3