Supplemental Problems

1.

Prove that if a matrix A has two identical rows (or columns) then its determinant is zero. (Hint: make use of elementary row and column operations)

2.

Suppose that the set of polynomials p₀(x), p₁(x), ... p_n(x) are such that the degree of p_k(x) is exactly equal to k. Prove that p₀(x), p₁(x), ... p_n(x) form a linearly independent set of functions (i.e. show their Wronskian is nonzero for a least one value of x).