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2.5 Given the set of vectors B=(p= (1, -2,1),u =(-1,2,-1),w= (-6,12,-6)) The dimension of the span of B is A0 C 3 D2

2.5 Given the set of vectors B=(p= (1, -2,1),u =(-1,2,-1),w= (-6,12,-6)) The dimension of the span of B is A0 C 3 D2

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 2CM: Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check...
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A ((-1,2), (3,-6)) B {(1,2), (5,3)) C ((1,3),(1,-1)} D ((1,0),(0,9)) 2.5 Given the set of vectors B = {v= (1, -2,1), u = (-1,2,-1),w= (-6,12,-6)) The dimension of the span of B is A0 B1 C3 D 2 2.6 Which of the following maps f: R → R³ is not linear? A f(x,y,z,w) = (0,0,0). B f(x,y,z,w) = (x,x+z,y+w). C f(x,y,z,w) = (1,0,1). D f(x,y,z,w)= (y.y.y). 2.7 The kernel of the linear map f: R³ R³ defined by f(x, y, z) = (x+ y.y+z,z+x) is A ker f= ((0,0,0)). B ker f = {(x,y,z) | x,y,z € R}. Cker f= {(2,2,2)). D ker f= {(1,1,1)). 2.8 Iff:R³ R is a linear map and dim(ker f) = 2 then A dim(Im f) = 1. B dim(Im f) = 2. C dim(Im f) = 3. D dim(Im f)=4. 2.9 If B (u (1,0,1), v= (0,1,1),w= (1,0,0)) is a basis of R³, then the first coordinate the vector x=(2,-4,3) in the basis B is: A a 1. Ba=7. Ca=5. Da=0. 2.10 State if the following statement is true or false. If V is a vector space of dimension n then any subset of V with more than n vectors is linearly dependant in V 2.11 State if the following statement is true or false. If V is a vector space of dimension n, where n> 3. then any set of n-2 is linearly independent
Transcribed Image Text:A ((-1,2), (3,-6)) B {(1,2), (5,3)) C ((1,3),(1,-1)} D ((1,0),(0,9)) 2.5 Given the set of vectors B = {v= (1, -2,1), u = (-1,2,-1),w= (-6,12,-6)) The dimension of the span of B is A0 B1 C3 D 2 2.6 Which of the following maps f: R → R³ is not linear? A f(x,y,z,w) = (0,0,0). B f(x,y,z,w) = (x,x+z,y+w). C f(x,y,z,w) = (1,0,1). D f(x,y,z,w)= (y.y.y). 2.7 The kernel of the linear map f: R³ R³ defined by f(x, y, z) = (x+ y.y+z,z+x) is A ker f= ((0,0,0)). B ker f = {(x,y,z) | x,y,z € R}. Cker f= {(2,2,2)). D ker f= {(1,1,1)). 2.8 Iff:R³ R is a linear map and dim(ker f) = 2 then A dim(Im f) = 1. B dim(Im f) = 2. C dim(Im f) = 3. D dim(Im f)=4. 2.9 If B (u (1,0,1), v= (0,1,1),w= (1,0,0)) is a basis of R³, then the first coordinate the vector x=(2,-4,3) in the basis B is: A a 1. Ba=7. Ca=5. Da=0. 2.10 State if the following statement is true or false. If V is a vector space of dimension n then any subset of V with more than n vectors is linearly dependant in V 2.11 State if the following statement is true or false. If V is a vector space of dimension n, where n> 3. then any set of n-2 is linearly independent
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