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Given the vectors u (1,2,3) and v (2,2,-1): (a) Determine u...
2) Given 3 vectors. 11 | u = 0 | u = -1 L2 a) What...
2) Given 3 vectors. 11 | u = 0 | u = -1 L2 a) What vector space do these vectors belong to? b) Geometrically describe the space spanned by vectors uj and u2. c) Is vector, v, in the subspace spanned by the vectors uj and u2? d) Are all 3 vectors linearly dependent or independent of each other? Explain why or why not. e) If possible, find the linear combination of vectors u; and uz that equals vector...
answer this . will rate after Given the vectors u = (1, -2,1), v= {5,–4,0) and...
answer this . will rate after
Given the vectors u = (1, -2,1), v= {5,–4,0) and w = (3,0,-2) (6 points) a) Graph u, v, and was position vectors and label each vector. Show your calculation or justify your reasoning (4 points) b) To the nearest degree, what is the angle between the vectors u and w. (6 points) c) Write the equation of the plane containing the vectors u and w (4 points) d) Determine if the vectors u,...
please help with this linear algebra question Question 10 [10 points] Let V be a vector...
please help with this linear algebra
question
Question 10 [10 points] Let V be a vector space and suppose that {u, v, w is an independent set of vectors in V. For each of the following sets of vectors, determine whether it is linearly independent or linearly dependent. If it is dependent, give a non-trivial linear combination of the vectors yielding the zero vector. a) {-v-3w, 2u+w, -u-2v} is linearly independent b) {-3v-3w, -u-w, -3u+3v} < Select an answer >
Problem 1. The figure below shows the vectors u, v, and w, along with the images...
Problem 1. The figure below shows the vectors u, v, and w, along with the images T(u) and T(v) to the right. Copy this figure, and draw onto it the image T(w) as accurately as possible. (Hint: First try writing w as a linear combination of u and v.) TV (u) Problem 2. Let u = | and v Suppose T : R2 + R2 is a linear transformation with 6 1 3) Tu = T(u) = -3 and T(v)...
Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle betwe...
Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle between v and w. (b) Consider the projection proj, w of w onto v, and then project this projection on u to get proju (proj, w). Is this necessarily equal to the projection proj, w of w on u? Prove or give a counterexample. (c) Find the volume of the parallelepiped with edges formed by u-(2,5,c), v (1,1,1) and w...
Find the volume of the parallelepiped spanned by the vectors u=〈3,−2,2〉, v=〈1,0,1〉, and w=〈−2,1,−5〉. Write the...
Find the volume of the parallelepiped spanned by the vectors u=〈3,−2,2〉, v=〈1,0,1〉, and w=〈−2,1,−5〉. Write the exact answer. Do not round.
3 - 2 Let u= Note that {u, v, w} is an orthogonal set of vectors...
3 - 2 Let u= Note that {u, v, w} is an orthogonal set of vectors and w - -3 4 9 be a vector in subspace W, where W = Span{u, v, w}. Let y= 11 -27 Write y as a linear combination of u, v, and uw, i.e. y = ciu + cqũ + c3W. Answer: y=
[1] In parallelogram WXYZ, if u joins X to Y and v joins X to W,...
[1] In parallelogram WXYZ, if u joins X to Y and v joins X to W, which connection forms a vector equal to u + v? v + u? u-v? V-u? A. W to Y B. Y to W C. X to Z D. Z to X W z Y [2] A linear combination of vectors is given. Determine the resultant vector using the tip- to-tail method for adding vectors geometrically. (9,-6) + (-12, -1) - (3, -15) + 5(2,...
1) 2) Use the vectors u = 2i - j, v = 21 - 3j, and...
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2)
Use the vectors u = 2i - j, v = 21 - 3j, and w = -3i + 5j to evaluate the expression. 2v - u + w Find a unit vector in the same direction as the given vector. a = 201 - 21j
6-7. Given vectors U = -41 +12). V = 5i - 21,W=-31 - 1 6. Find...
6-7. Given vectors U = -41 +12). V = 5i - 21,W=-31 - 1 6. Find a) 30 - 5.b) |2V - WI 7. a) U. W What can you tell from the result? b) angle between U and keep one digit after decimal, calculator ok) 8. a) Write the complex number -2 -21 in trigonometry form. Be sure to graph when looking for O. (No decimal answer) b) use the result from a) and De Moivre's theorem the find...
2) Given 3 vectors. 11 | u = 0 | u = -1 L2 a) What vector space do these vectors belong to? b) Geometrically describe the space spanned by vectors uj and u2. c) Is vector, v, in the subspace spanned by the vectors uj and u2? d) Are all 3 vectors linearly dependent or independent of each other? Explain why or why not. e) If possible, find the linear combination of vectors u; and uz that equals vector...
answer this . will rate after
Given the vectors u = (1, -2,1), v= {5,–4,0) and w = (3,0,-2) (6 points) a) Graph u, v, and was position vectors and label each vector. Show your calculation or justify your reasoning (4 points) b) To the nearest degree, what is the angle between the vectors u and w. (6 points) c) Write the equation of the plane containing the vectors u and w (4 points) d) Determine if the vectors u,...
please help with this linear algebra
question
Question 10 [10 points] Let V be a vector space and suppose that {u, v, w is an independent set of vectors in V. For each of the following sets of vectors, determine whether it is linearly independent or linearly dependent. If it is dependent, give a non-trivial linear combination of the vectors yielding the zero vector. a) {-v-3w, 2u+w, -u-2v} is linearly independent b) {-3v-3w, -u-w, -3u+3v} < Select an answer >
Problem 1. The figure below shows the vectors u, v, and w, along with the images T(u) and T(v) to the right. Copy this figure, and draw onto it the image T(w) as accurately as possible. (Hint: First try writing w as a linear combination of u and v.) TV (u) Problem 2. Let u = | and v Suppose T : R2 + R2 is a linear transformation with 6 1 3) Tu = T(u) = -3 and T(v)...
Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle between v and w. (b) Consider the projection proj, w of w onto v, and then project this projection on u to get proju (proj, w). Is this necessarily equal to the projection proj, w of w on u? Prove or give a counterexample. (c) Find the volume of the parallelepiped with edges formed by u-(2,5,c), v (1,1,1) and w...
3 - 2 Let u= Note that {u, v, w} is an orthogonal set of vectors and w - -3 4 9 be a vector in subspace W, where W = Span{u, v, w}. Let y= 11 -27 Write y as a linear combination of u, v, and uw, i.e. y = ciu + cqũ + c3W. Answer: y=
[1] In parallelogram WXYZ, if u joins X to Y and v joins X to W, which connection forms a vector equal to u + v? v + u? u-v? V-u? A. W to Y B. Y to W C. X to Z D. Z to X W z Y [2] A linear combination of vectors is given. Determine the resultant vector using the tip- to-tail method for adding vectors geometrically. (9,-6) + (-12, -1) - (3, -15) + 5(2,...
1)
2)
Use the vectors u = 2i - j, v = 21 - 3j, and w = -3i + 5j to evaluate the expression. 2v - u + w Find a unit vector in the same direction as the given vector. a = 201 - 21j
6-7. Given vectors U = -41 +12). V = 5i - 21,W=-31 - 1 6. Find a) 30 - 5.b) |2V - WI 7. a) U. W What can you tell from the result? b) angle between U and keep one digit after decimal, calculator ok) 8. a) Write the complex number -2 -21 in trigonometry form. Be sure to graph when looking for O. (No decimal answer) b) use the result from a) and De Moivre's theorem the find...
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