Linear Combination

(1) Draw the vectors



on a graph.

(2) The vectors



are linearly dependent. Explain why.

(3) Suppose the vectors



are linearly independent. Write the meaning of this as a vector equation, and then write the vector equation as a matrix equation.

(4) The vectors



must be linearly dependent. Give a reason.

(5) Use your answer to (4) to deduce that the polynomials



must be linearly dependent.