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...

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

Expert Solution

plz feel free to comment in case of doubts as i am happy to help you. Plz upvote the solution if u r satisfied. It means a lot to me. Thanks

Colby Messinger answered 4 months ago

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

#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?

V1 V2 V3 V4 V1 1.0 V2 .27 1.0 V3 -.13 .65 1.0 V4 .20 -.15...

V1 V2 V3 V4 V1 1.0 V2 .27 1.0 V3 -.13 .65 1.0 V4 .20 -.15 -.72 1.0 IN THIS EXERCISE, YOU WILL SEE A CORRELATION MATRIX. EXAMINE THE MATRIX AND ANSWER THE QUESTIONS THAT FOLLOW. 1. Which two variables have the strongest (largest) relationship? 2. Which two variables have the weakest (smallest) relationship? 3. Which two variables have the strongest positive relationship? 4. which two variables have the stronger negative relationship? 5. Which two variables have the weakest positive...

v1=[0,1,4] v2=[-4,-5,7] v3=[14,10,8] b=[16,18,19]. Let v1,v2, and v3 be three nonzero vectors in R3. Suppose v2...

v1=[0,1,4] v2=[-4,-5,7] v3=[14,10,8] b=[16,18,19]. Let v1,v2, and v3 be three nonzero vectors in R3. Suppose v2 is not a scalar multiple of either v1 or v3 and v3 is not a scalar multiple of either v1 or v2. Does it follow that every vector in R3 is in span{v1,v2,v3}?

Are the vectors v1 = (1 , 2, 3), v2 = (2, 4, 6), and v3...

Are the vectors v1 = (1 , 2, 3), v2 = (2, 4, 6), and v3 = (1, 1, 3) linearly independent or dependent? Since v2 is a scalar multiple of v1, both v1 and v2 are linearly dependent, but what does that say about the linear dependence of the three vectors as a whole?

If {v1, v2, v3, v4} is a linearly-independent subset of a vector space V over the...

If {v1, v2, v3, v4} is a linearly-independent subset of a vector space V over the field Q, is the set {3v1 + 2v2 + v3 + v4, 2v1 + 5v2, 3v3 + 2v4, 3v1 + 4v2 + 2v3 + 3v4} linearly independent as well?

Java Write a method intersect_or_union_fcn() that gets vectors of type integer v1, v2, and v3 and...

Java Write a method intersect_or_union_fcn() that gets vectors of type integer v1, v2, and v3 and determines if the vector v3 is the intersection or union of vectors v1 and v2. Example 1: If v1 = {2, 3, 1, 5}, v2 = {3, 4, 5} and v3 = {3, 5}, then: intersect_or_union_fcn(v1, v2, v3) will print: v3 is the intersection of v1 and v2 Example 2: If v1 = {2, 3, 1, 5}, v2 = {3, 4, 5}...

consider the subspace W=span[(4,-2,1)^T,(2,0,3)^T,(2,-4,-7)^T] Find A) basis of W B) Dimension of W C) is vector...

consider the subspace W=span[(4,-2,1)^T,(2,0,3)^T,(2,-4,-7)^T] Find A) basis of W B) Dimension of W C) is vector v=[0,-2,-5]^T contained in W? if yes espress as linear combantion

Let W be a subspace of R^n and suppose that v1,v2,w1,w2,w3 are vectors in W. Suppose...

Let W be a subspace of R^n and suppose that v1,v2,w1,w2,w3 are vectors in W. Suppose that v1; v2 are linearly independent and that w1;w2;w3 span W. (a) If dimW = 3 prove that there is a vector in W that is not equal to a linear combination of v1 and v2. (b) If w3 is a linear combination of w1 and w2 prove that w1 and w2 span W. (c) If w3 is a linear combination of w1 and...

a, The vectors v1 = < 0, 2, 1 >, v2 = < 1, 1, 1...

a, The vectors v1 = < 0, 2, 1 >, v2 = < 1, 1, 1 > , v3 = < 1, 2, 3 > , v4 = < -2, -4, 2 > and v5 = < 3, -2, 2 > generate R^3 (you can assume this). Find a subset of {v1, v2, v3, v4, v5} that forms a basis for R^3. b. v1 = < 1, 0, 0 > , v2 = < 1, 1, 0 > and v3...

Question