Question
In: Advanced Math
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?
Solutions
Expert Solution
Concept : If one vector can be expressed a linear combination of another vectors , then those vectors can be said as Linearly dependent.
If v2 can be expressed as linear combination of v1 and v3 such that,
v2 = a1V1 + a2V2 where at least one of the scalar a1, a2 is non zero
Here,
v2 = 2v1 + 0v3 . Thus , all three vectors are Linearly dependent.
Method 2 :
Colby Messinger answered 2 years agoRelated Solutions
if {v1,v2,v3} is a linearly independent set of vectors, then {v1,v2,v3,v4} is too.
if {v1,v2,v3} is a linearly independent set of vectors, then
{v1,v2,v3,v4} is too.
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}?
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
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}...
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...
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...
#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?
mass v1 v2 v3 1 1.1 1.24 0.98 2 1.53 1.46 1.57 3 1.96 1.83 1.79...
mass
v1
v2
v3
1
1.1
1.24
0.98
2
1.53
1.46
1.57
3
1.96
1.83
1.79
4
2.14
2.16
2.35
5
2.4
2.52
2.5
Using excel, how do you find the t test and the chi-squared?
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 .
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Non-constant growth model: Do=$2.00 required return on equity= 5% g= 9% n=1,2 g=7% n=3,4 g=3% n=5...
- . Find all x ∈ Z143 such that x2Ξ 7 (mod 143). Please explain all steps...
- #Python: A palindrome is a sequence of characters that reads the same backwards as forwards. For...
- Explain an example in which a variable has two different addresses at different places in a...
- Hadley, a thirty-five-year-old physician, has worked at Princeton Plainsboro Hospital for six years. She recently received...
- QUESTION 1. For each of the following, state whether the occurrence of the variable x occurs...
- According to Mike Taft of RVK, the “Markets Group” is an important unit of the Federal...
ADVERTISEMENT