Given the vectors (1, 0, 1) and (1, 2, -3). Write the steps necessary to show that these vectors form a basis for R. If

Given the vectors (1, 0, 1) and (1, 2, -3). Write the steps necessary to show that these vectors form a basis for R³. If the vectors do not form a basis for R³, state the reason(s) why. Your steps should make use of spanning and linearly independence. From your analysis, give a clear and concise conclusion. Also as an addendum, include what defines a "linear algebra" and give two examples. Does your conclusion make sense? Please explain.