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Complete the proof of Property 4 of the following theorem by supplying the justification for each step, Properties of Additive Identity and Additive Inverse Let 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, il v uv, then u-0. 2. The additive inverse of v is unique. That is, if v+u-0, then u--v. 3. Ov=0 đi cho 5. If cv = 0, then c-0 or v=0. 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. uv is a vector in R. 2.u+v=v+u 3. (uu) +w-u+(u+w) 4.u+0-u 5.u+(-u)-0 6. cu is a vector in R 7. c(u + v) cu + CV 8. (c+d)ucu + du 9. c(du) = (cd)u 10. 1(u)- u Step co= c(0+0) coco+co co+ (-c0) (co+co) + (-co) 0(c0c0) + (-co) 0c0+ (co(-co)) min10 0=co -Select- Select -Select- -Select- Select Select- -Select- Justification Closure under addition Commutative property of addition Associative property of addition Additive identity property Additive inverse property Closure under scalar multiplication Distributive property Distributive property Associative property of multiplication Multiplicative identity property >

Complete the proof of Property 4 of the following theorem by supplying the justification for each step, Properties of Additive Identity and Additive Inverse Let 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, il v uv, then u-0. 2. The additive inverse of v is unique. That is, if v+u-0, then u--v. 3. Ov=0 đi cho 5. If cv = 0, then c-0 or v=0. 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. uv is a vector in R. 2.u+v=v+u 3. (uu) +w-u+(u+w) 4.u+0-u 5.u+(-u)-0 6. cu is a vector in R 7. c(u + v) cu + CV 8. (c+d)ucu + du 9. c(du) = (cd)u 10. 1(u)- u Step co= c(0+0) coco+co co+ (-c0) (co+co) + (-co) 0(c0c0) + (-co) 0c0+ (co(-co)) min10 0=co -Select- Select -Select- -Select- Select Select- -Select- Justification Closure under addition Commutative property of addition Associative property of addition Additive identity property Additive inverse property Closure under scalar multiplication Distributive property Distributive property Associative property of multiplication Multiplicative identity property >

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.1: Vector In R^n
Problem 61E: Illustrate properties 110 of Theorem 4.2 for u=(2,1,3,6), v=(1,4,0,1), w=(3,0,2,0), c=5, and d=2....
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Complete the proof of Property 4 of the following theorem by supplying the justification for each step, Properties of Additive Identity and Additive Inverse Let v be a vector in R", and let c be a scolar. Then the properties below are true. 1. The additive identity is unique. That is, if v uv, then u - 0. 2. The additive inverse of v is unique. That is, if v +u0, then u 3. Ov=0 đi ch 5. If cv = 0, then c = 0 or v=0. 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. uv is a vector in R 2.u+v v+U 3. (uu)+w-u (uw) 4.U+0=U 5. u + (-u) 0 6. cu is a vector in R. Step co= c(0+0) 7. c(u + v) cu + CV 8. (c+d)ucu + du - 9. c(du) = (cd)u 10. 1(u)- u 0-c0 coco+co co + (-00) - (co + c0) + (-c0) 0 (c0c0) + (-co) 0c0 (co(-co))) 0 0 -Select- Select- -Select- -Select- Select- Select -Select- Justification Closure under addition Commutative property of addition Associative property of addition Additive identity property Additive inverse property Closure under scalar multiplication Distributive property Distributive property Associative property of multiplication Multiplicative Identity property
Transcribed Image Text:Complete the proof of Property 4 of the following theorem by supplying the justification for each step, Properties of Additive Identity and Additive Inverse Let v be a vector in R", and let c be a scolar. Then the properties below are true. 1. The additive identity is unique. That is, if v uv, then u - 0. 2. The additive inverse of v is unique. That is, if v +u0, then u 3. Ov=0 đi ch 5. If cv = 0, then c = 0 or v=0. 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. uv is a vector in R 2.u+v v+U 3. (uu)+w-u (uw) 4.U+0=U 5. u + (-u) 0 6. cu is a vector in R. Step co= c(0+0) 7. c(u + v) cu + CV 8. (c+d)ucu + du - 9. c(du) = (cd)u 10. 1(u)- u 0-c0 coco+co co + (-00) - (co + c0) + (-c0) 0 (c0c0) + (-co) 0c0 (co(-co))) 0 0 -Select- Select- -Select- -Select- Select- Select -Select- Justification Closure under addition Commutative property of addition Associative property of addition Additive identity property Additive inverse property Closure under scalar multiplication Distributive property Distributive property Associative property of multiplication Multiplicative Identity property
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