Complete the proof to the right that the zero vector is unique.Suppose that w in V has the property that u + w= w +u=u for all u in V. In particular, 0 +w = 0. But 0+ w =w+0 by Axiom and w+0=w by AxiomAxiomsIn the following axioms, u, v, and w are in vector space V and c and d are scalars.|. Hence, w =w +0 =0 +w = 0.(Type whole numbers.)1. The sumu+v is in V.2. u+v=v +u3. (u+v) + w =u+ (v+ w)4. V has a vector 0 such that u +0=u.5. For each u in V, there is a vector - u in V such that u + (-u) =0.6. The scalar multiple cu is in V.7. c(u + v) = cu + cv8. (c+d)u = cu + du9. c(du) = (cd)u10.1u =u

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Complete the proof to the right that the zero vector is unique. Suppose that w in V has the property that u+w=w+uu for all u in V. In particular, 0 +w=0. But 0+ w =w+O by Axiom and w+0-w by Axiom Hence, w=w+0=0+w=0. (Type whole numbers.) Axioms In the following axioms, u, v, and w are in vector space V and c and d are scalars. 1. The sum uvis in V. 2. u+v=v+u 3. (uv)wu (vw) 4. V has a vector O such that u+ 0=u 5. For each u in V, there is a vector -u in V such that u+(-u)=0. 6. The scalar multiple cu is in V. 7. c(u+ v)= cu +cv 8. (c+dju cu+ du 9. c(du) = (odju 10. 1uu

Complete the proof to the right that the zero vector is unique. Suppose that w in V has the property that u+w=w+uu for all u in V. In particular, 0 +w=0. But 0+ w =w+O by Axiom and w+0-w by Axiom Hence, w=w+0=0+w=0. (Type whole numbers.) Axioms In the following axioms, u, v, and w are in vector space V and c and d are scalars. 1. The sum uvis in V. 2. u+v=v+u 3. (uv)wu (vw) 4. V has a vector O such that u+ 0=u 5. For each u in V, there is a vector -u in V such that u+(-u)=0. 6. The scalar multiple cu is in V. 7. c(u+ v)= cu +cv 8. (c+dju cu+ du 9. c(du) = (odju 10. 1uu

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.2: Inner Product Spaces

Problem 101E: Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that...

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