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Given vector space V and W, is V a subspace of W?

Given vector space V and W, is V a subspace of W?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter3: Triangles
Section3.5: Inequalities In A Triangles
Problem 35E: Prove by the indirect method: Given: MPN is not isosceles Prove: PMPN
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Given vector space V and W, is V a subspace of W? 

4d. Let a, bEe such that JS la (his implies that independent. a-0, b=0. Hence {1 0)T, CO )7} is linearly Let )EW be arb itrary element, where Zi,Zu E C an to - 3. (0) + zz(), which Bs linear gimbmation if the elements of the set {CI 0)7, co 1)73 to Stnce C) EW is an arbitrary element, therefore every element ot he vector space W = linear zombination A the liset f Cr 0);co )?}. ho bo) mail {()z,2.6 (3 can be writhen as Henze, the set { CI 0)T, COUD'} form a basis for the vecter W= (? CC)={() ,7, E C} . Dimenslon of the vector space W, dim CW) = 2 pace
Transcribed Image Text:4d. Let a, bEe such that JS la (his implies that independent. a-0, b=0. Hence {1 0)T, CO )7} is linearly Let )EW be arb itrary element, where Zi,Zu E C an to - 3. (0) + zz(), which Bs linear gimbmation if the elements of the set {CI 0)7, co 1)73 to Stnce C) EW is an arbitrary element, therefore every element ot he vector space W = linear zombination A the liset f Cr 0);co )?}. ho bo) mail {()z,2.6 (3 can be writhen as Henze, the set { CI 0)T, COUD'} form a basis for the vecter W= (? CC)={() ,7, E C} . Dimenslon of the vector space W, dim CW) = 2 pace
Date: 4e- let a,b,c;d E IR such that Latui. to This implies thata=0, b=0, c=0,d-0. Hence the set {CI 0JT, CO 1)T, li 0)T, (o i)} is line arly independent. Lt ()()をVbe an 31 a+ ib arbitrary element, where a,b, c,d EIR Tbere fore , A eun be written as which is linear combinaflan of the elements of the set { CI o)T, CO DT,li 0), co i)}. arbltrary element, therefore every elemont こ was an oA the vertor gpace V = C°CR - {(2)]2, ,2, EC3 ean be written as as linear combination # the set {CI 07T, CO 1, Ci 0)T, CO i)T! Hence, the set {CIO', CO1, li 0)", co )" form a basis for the vector space V=c? CIR) - { (2,,3,Ee}. %3D Dimensfon of vector space V, dim cv) =4
Transcribed Image Text:Date: 4e- let a,b,c;d E IR such that Latui. to This implies thata=0, b=0, c=0,d-0. Hence the set {CI 0JT, CO 1)T, li 0)T, (o i)} is line arly independent. Lt ()()をVbe an 31 a+ ib arbitrary element, where a,b, c,d EIR Tbere fore , A eun be written as which is linear combinaflan of the elements of the set { CI o)T, CO DT,li 0), co i)}. arbltrary element, therefore every elemont こ was an oA the vertor gpace V = C°CR - {(2)]2, ,2, EC3 ean be written as as linear combination # the set {CI 07T, CO 1, Ci 0)T, CO i)T! Hence, the set {CIO', CO1, li 0)", co )" form a basis for the vector space V=c? CIR) - { (2,,3,Ee}. %3D Dimensfon of vector space V, dim cv) =4
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