4. Solve the following. (a) Determine which standard basis vectors can be added to the set S = {(-1,4,3), (1,–4,2)} to produce a basis for R³. (b) Remove one vector from the set S = {(1,0,3), (1,0,0), (2, 0, 6), (2, 1, 8)} so that it forms a basis for R3.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.