#1 Let H= Span{v1,v2,v3,v4}. For each of the following sets of vectors determine whether H is...

#1 Let H= Span{v1,v2,v3,v4}. For each of the following sets of vectors determine whether H is a line, plane ,or R3. Justify your answers.

(a)v1= (1,2,−2),v2= (7,−7,−7),v3= (16,−12,−16),v4= (0,−3,−3)

(b)v1= (2,2,2),v2= (6,6,5),v3= (−16,−16,−14),v4= (28,28,24)

(c)v1= (−1,3,−3),v2= (0,0,0),v3= (−2,6,−6),v4= (−3,9,−9)

#2 Plot the linesL1: x= t[4−1] and L2: x= [−4−2] + t[4−1] using their vector forms. If[12k]is onL2. What is the value of k?

Expert Solution

Colby Messinger answered 2 years ago

if {v1,v2,v3} is a linearly independent set of vectors, then {v1,v2,v3,v4} is too.

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consider the vectors: v1=(1,1,1) v2=(2,-1,1) v3=(3,0,2) v4=(6,0,4) a)find the dimension and a basis W=Span(v1,v2,v3,v4) b) Does the vector v=(3,3,1) belong to W. Justify your answer c) Is it true that W=Span(v3,v4)? Justify your answer

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