Complete the proof of Property 4 of the following theorem by supplying the justification for each step.Properties of Additive Identity and Additive InverseLet v be a vector in R", and let c be a scalar. Then the properties below are true.1. The additive identity is unique. That is, if v + u = v, then u = 0.2. The additive inverse of v is unique. That is, if v + u = 0, then u = -v.3. Ov = 04. co = 05. If cv =0, then c = 0 or v = 0.6. -(-v) =Use the properties of vector addition and scalar multiplication from the following theorem.Properties of Vector Addition and Scalar Multiplication in R"Let u, v, and w be vectors in R", and let c and d be scalars.1. u + v is a vector in R".Closure under addition2. u + v = v + uCommutative property of additionAssociative property of additionAdditive identity propertyAdditive inverse propertyClosure under scalar multiplicationDistributive propertyDistributive propertyAssociative property of multiplicationMultiplicative identity property3. (u + u) + w = u + (u + w)4. u + 0 = u5. u + (-u) = 06. cu is a vector in R".7. c(u + v) = cu + cv8. (с + d)u9. c(du) = (cd)u10. 1(u) = u= cu + du%3DStepJustificationC =c(0 + 0)distributive propertycO = c0 + códistributive propertyc0 + (-c0) = (c0 + c0) + (-c0)add -c0 to both sides0 =(c0 + c0) + (-co)commutative property of additionO = c0 + (c0 + (-c0))additive inverse property0 = c0 + 0commutative property of addition0 = c0multiplicative identity property

Question

Complete the proof of Property 4 of the following theorem by supplying the justification for each step.Properties of Additive Identity and Additive InverseLet v be a vector in R&#34;, and let c be a scalar. Then the properties below are true.1. The additive identity is unique. That is, if v + u = v, then u = 0.2. The additive inverse of v is unique. That is, if v + u = 0, then u = -v.3. Ov = 04. co = 05. If cv =0, then c = 0 or v = 0.6. -(-v) =Use the properties of vector addition and scalar multiplication from the following theorem.Properties of Vector Addition and Scalar Multiplication in R&#34;Let u, v, and w be vectors in R&#34;, and let c and d be scalars.1. u + v is a vector in R&#34;.Closure under addition2. u + v = v + uCommutative property of additionAssociative property of additionAdditive identity propertyAdditive inverse propertyClosure under scalar multiplicationDistributive propertyDistributive propertyAssociative property of multiplicationMultiplicative identity property3. (u + u) + w = u + (u + w)4. u + 0 = u5. u + (-u) = 06. cu is a vector in R&#34;.7. c(u + v) = cu + cv8. (с + d)u9. c(du) = (cd)u10. 1(u) = u= cu + du%3DStepJustificationC =c(0 + 0)distributive propertycO = c0 + códistributive propertyc0 + (-c0) = (c0 + c0) + (-c0)add -c0 to both sides0 =(c0 + c0) + (-co)commutative property of additionO = c0 + (c0 + (-c0))additive inverse property0 = c0 + 0commutative property of addition0 = c0multiplicative identity property

Accepted Answer

Answered: Image /qna-images/answer/1cfe3073-01a7-484f-8bb7-c514c1bf9626.jpg