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

Expert Solution

Colby Messinger answered 2 years ago

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?

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...

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

#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=[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?

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}...

Determine whether the members of the given set of vectors are linearly independent. If they are...

Determine whether the members of the given set of vectors are linearly independent. If they are linearly dependent, find a linear relation among them of the form c1x(1) + c2x(2) + c3x(3) = 0. (Give c1, c2, and c3 as real numbers. If the vectors are linearly independent, enter INDEPENDENT.) x(1) = 9 1 0 , x(2) = 0 1 0 , x(3) = −1 9 0

Let v1 = [-0.5 , v2 = [0.5 , and v3 = [-0.5 -0.5 -0.5 ...

Let v1 = [-0.5 , v2 = [0.5 , and v3 = [-0.5 -0.5 -0.5 0.5 0.5 0.5 0.5 -0.5] 0.5] 0.5] Find a vector v4 in R4 such that the vectors v1, v2, v3, and v4 are orthonormal.

(a) If V1,V2⊂V show that (V2^⊥)⊂(V1^⊥) implies V1⊂V2 (b) If V1,V2⊂V , show that (V1+V2)^⊥=(V1^⊥)∩(V2^⊥) where...

(a) If V1,V2⊂V show that (V2^⊥)⊂(V1^⊥) implies V1⊂V2 (b) If V1,V2⊂V , show that (V1+V2)^⊥=(V1^⊥)∩(V2^⊥) where we write V1+V2 to be the subspace of V spanned by V1 and V2 .

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