MATB24H3 Study Guide - Final Guide: Scalar Multiplication, Euclidean Vector, Linear Combination
Document Summary
Therefore p2 is a subspace of p3. theorem 0. 3 test for a subspace: let v, , is a vector space. Then: it contains the zero vector from property a3 of the properties of vector spaces. Thus it is nonempty: it is closed under addition and. 1: it is closed under scalar multiplication ( =) assume that w satis es the three properties above. Then w satis es the rst two conditions of vector spaces. X: r1v1 + r2v2 + + rkvk = 0 implies that r1 = r2 = = rk = 0. Since p1(x) p2(x) p3(x) = 0 then x is linearly dependent. We want to determine if r1 sin x + r2ex + r3 cos x = 0 has a nontrivial solution. Method 1: evaluate (*) for di erent x to get 3 equations in 3 unknowns at x = x = 0.
