Show that if A is symmetric, then ||-4||2 = p(A).

M303 Section 4.5 Notes- The Dimension of a Vector Space 11-16-16 If is a vector space with 2 bas1s 2 , , is it true that they have the same number of elements o In notation, want to determine if #1 = # 2 o Note: for nonzero vector space, infinite number of bases exist (scalar multiples of basis are still bases) o For = ℝ , this is true; all bases must have elements (matrix must have vectors in ℝ ) to be linearly independent and span Theorem 9- If is a vector space and = , ,…, }is a basis with elements, then any set in with more than elements must be linearly dependent o Proof: Let {