Let {v1, v2,v3} be a linearly independent set in R^n and let v = -αv3 +v1,w...
Let {v1, v2,v3} be a linearly independent set in R^n and let v = -αv3 +v1,w = v2 - αv1, u= v3-αv2 where αER, find all the values of α, where v, w, u are linearly dependent. do not use matrices.
Homework Answers
Add Answer to:
Let {v1, v2,v3} be a linearly independent set in R^n and let v =
-αv3 +v1,w...
Let v1,v2,v3 and v4 be linearly independent vectors in R4. Determine whether each set of vectors...
Let v1,v2,v3 and v4 be linearly independent vectors in R4.
Determine whether each set of vectors is linearly independent or
dependent. Please solve d) and f)
U1, 2, 03, 4
1) Determine if w is in the subspace spanned by v1, v2, v3 2) Are the...
1) Determine if w is in the subspace spanned by v1, v2,
v3
2) Are the vectors v1, v2, v3 linearly dependent or
independent? justify your answer
Question 2. (15 pts) Let vi=(-3 0 6)", v2= (-2 2 3]", V3= (0 - 6 37, and w= [1 11 9". (1). Determine if w is in the subspace spanned by V1, V2, V3. (2). Are the vectors V1, V2, V3 linearly dependent or independent? Justify your answer
Let v1 and v2 be two arbitrary linearly independent vectors in R^n . Are (v1 +...
Let v1 and v2 be two arbitrary linearly independent vectors in R^n . Are (v1 + v2) and (v1 − v2) necessarily linearly independent? Justify.
(4 points) Let Are the vectors V1, V2 and V3 linearly independent? choose If the vectors...
(4 points) Let Are the vectors V1, V2 and V3 linearly independent? choose If the vectors are independent, enter zero in every answer blank since zeros are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. 1-1 Note: In order to get credit for this problem all answers must be correct.
suppose that s=(v1,v2,......vm) is a finite set of linearly independent vectors in V, and w ∈ V some other vector. Let T= S ∪ (W). Prove that T is not linearly independent if and only if w∈ span(s).
suppose that s=(v1,v2,......vm) is a finite set of linearly independent vectors in V, and w ∈ V some other vector. Let T= S ∪ (W). Prove that T is not linearly independent if and only if w∈ span(s).
חו (1 point) Suppose V1, V2, V3 is an orthogonal set of vectors in R Let...
חו (1 point) Suppose V1, V2, V3 is an orthogonal set of vectors in R Let w be a vector in span(V1, V2, V3) such that (v1,vi) = 24, (v2,v2) = 21, (V3, V3) = 9, (w,v) 120, (w, v2) = 147, (w,v3) -36, Vi+ V2+ then w= V3.
Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in span(V1, V2, V3) such that
Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in span(V1, V2, V3) such that (V1, V1) = 51, (V2, V2) = 638, (V3, V3) = 36, (w, V1) = 153, (w, v2) = 4466, (w, V3) = -36, then W = _______ V1 + _______ V2+ _______ V3.
Can I get help with questions 2,3,4,6? be the (2) Determine if the following sequences of vectors vi, V2, V3 are linear...
Can I get help with questions 2,3,4,6?
be the (2) Determine if the following sequences of vectors vi, V2, V3 are linearly de- pendent or linearly independent (a) ces of V 0 0 V1= V2 = V3 = w. It (b) contains @0 (S) V1= Vo= Va (c) inations (CE) n m. -2 VI = V2= V3 (3) Consider the vectors 6) () Vo = V3 = in R2. Compute scalars ,2, E3 not all 0 such that I1V1+2V2 +r3V3...
Problem 5: Let V and W be vector spaces and let B = {V1, V2, ...,...
Problem 5: Let V and W be vector spaces and let B = {V1, V2, ..., Un} CV be a basis for V. Let L :V + W be a linear transformation, and let Ker L = {2 € V: L(x)=0}. (a) If Ker L = {0}, show that C = {L(v1), L(02), ..., L(vn) } CW is a linearly independent set in W. (b) If C = {L(01), L(V2),..., L(Un)} C W is a linearly independent set in W,...
Let V be a vector space. Suppose dimV = n and {V1, V2, ..., Vn} is...
Let V be a vector space. Suppose dimV = n and {V1, V2, ..., Vn} is a basis of V. Thei which of the following is always true? a) Any set of n vectors is linearly dependent b) Any linearly dependent set in V is not part of basis c) Any linearly dependent set with n - 1 vectors is a basis d) A linearly independent set with n vectors is a basis
Let v1,v2,v3 and v4 be linearly independent vectors in R4.
Determine whether each set of vectors is linearly independent or
dependent. Please solve d) and f)
U1, 2, 03, 4
1) Determine if w is in the subspace spanned by v1, v2,
v3
2) Are the vectors v1, v2, v3 linearly dependent or
independent? justify your answer
Question 2. (15 pts) Let vi=(-3 0 6)", v2= (-2 2 3]", V3= (0 - 6 37, and w= [1 11 9". (1). Determine if w is in the subspace spanned by V1, V2, V3. (2). Are the vectors V1, V2, V3 linearly dependent or independent? Justify your answer
(4 points) Let Are the vectors V1, V2 and V3 linearly independent? choose If the vectors are independent, enter zero in every answer blank since zeros are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. 1-1 Note: In order to get credit for this problem all answers must be correct.
חו (1 point) Suppose V1, V2, V3 is an orthogonal set of vectors in R Let w be a vector in span(V1, V2, V3) such that (v1,vi) = 24, (v2,v2) = 21, (V3, V3) = 9, (w,v) 120, (w, v2) = 147, (w,v3) -36, Vi+ V2+ then w= V3.
Can I get help with questions 2,3,4,6?
be the (2) Determine if the following sequences of vectors vi, V2, V3 are linearly de- pendent or linearly independent (a) ces of V 0 0 V1= V2 = V3 = w. It (b) contains @0 (S) V1= Vo= Va (c) inations (CE) n m. -2 VI = V2= V3 (3) Consider the vectors 6) () Vo = V3 = in R2. Compute scalars ,2, E3 not all 0 such that I1V1+2V2 +r3V3...
Problem 5: Let V and W be vector spaces and let B = {V1, V2, ..., Un} CV be a basis for V. Let L :V + W be a linear transformation, and let Ker L = {2 € V: L(x)=0}. (a) If Ker L = {0}, show that C = {L(v1), L(02), ..., L(vn) } CW is a linearly independent set in W. (b) If C = {L(01), L(V2),..., L(Un)} C W is a linearly independent set in W,...
Let V be a vector space. Suppose dimV = n and {V1, V2, ..., Vn} is a basis of V. Thei which of the following is always true? a) Any set of n vectors is linearly dependent b) Any linearly dependent set in V is not part of basis c) Any linearly dependent set with n - 1 vectors is a basis d) A linearly independent set with n vectors is a basis
Most questions answered within 3 hours.
-
What mechanisms Drive speciation??
(I.e. what was Dawins theory on the orgin of species, and how...
asked 1 hour ago -
The manager at a car assembly plant believes that the mean
assembly time for a car...
asked 2 hours ago -
Which of the following is true of electron capture?
A) It decreases the nuclide's mass number...
asked 3 hours ago -
Assuming an efficiency of 43.10%, calculate the actual yield of
magnesium nitrate formed from 114.9 g...
asked 4 hours ago -
The highly pathogenic bacterium Clostridium
perfringens causes gangrene, a disease that results in the
destruction of...
asked 5 hours ago -
In the context of situation analysis, which of the following is
a category for analysis in...
asked 5 hours ago -
In a study of the gas phase decomposition of sulfuryl chloride
at 600 K SO2Cl2(g)SO2(g) +...
asked 6 hours ago -
75 g of 2-propanol (C3H8O) and 25 g of pentane are mixed in a
200 mL...
asked 6 hours ago -
The 2800-turn coil in a dc motor has an area per turn of 1.1 ×
10-2...
asked 6 hours ago -
Draw a combinational logic circuit diagram with a symbol inside
the box for two I/P of...
asked 6 hours ago -
The cliché we use quite a lot in finance is: there is a need to
maximize...
asked 6 hours ago -
In class we discussed the addition of HCl to alpha pinene. Would
you expect one or...
asked 6 hours ago