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detailed work pls axb. Find the angle Let a, b 0 be vectors in R3 with...
(4) Let F be a field and let a, b E F with a 0. Show that Fx/axb)F (4) Let F be a field and let a, b E F with a 0....
(4) Let F be a field and let a, b E F with a 0. Show that Fx/axb)F
(4) Let F be a field and let a, b E F with a 0. Show that Fx/axb)F
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...
b) Let a R3 be a vector of length 1. Define H={x E R3 : a·x=0). Here a x denotes the dot product of the vectors a and x. (i) Show that H is a subgroup of R (ii) For λ E R, show that : a·x= is a co...
b) Let a R3 be a vector of length 1. Define H={x E R3 : a·x=0). Here a x denotes the dot product of the vectors a and x. (i) Show that H is a subgroup of R (ii) For λ E R, show that : a·x= is a coset of H in R3. (ii) Is H cyclic? Prove or disprove.
b) Let a R3 be a vector of length 1. Define H={x E R3 : a·x=0). Here a x...
2 5 Do the vectors u = and v= 3 7 span R3? -1 1 Explain! Hint: Use Let a, a2,ap be vectors in R", let A = [a1a2..ap...
2 5 Do the vectors u = and v= 3 7 span R3? -1 1 Explain! Hint: Use Let a, a2,ap be vectors in R", let A = [a1a2..ap The following statements are equivalent. 1. ai,a2,..,a, span R" = # of rows of A. 2. A has a pivot position in every row, that is, rank(A) Select one: Oa. No since rank([uv]) < 2 3=# of rows of the matrix [uv b.Yes since rank([uv]) =2 = # of columns of...
Let S be the tetrahedron in R3 with vertices at x the vectors 0, e1, e2, and e3, and let S' be the tetrahedron with...
Let S be the tetrahedron in R3 with vertices at x the vectors 0, e1, e2, and e3, and let S' be the tetrahedron with vertices at vectors 0, v1, V2 and v3. See the figures to the right. Complete parts (a) and (b) below. a. Describe a linear transformation that maps S onto S lf T is a linear transformation that maps S onto S, then the standard matrix for T, written in terms of v1-v2, and v3, is...
Question (7) Consider the vector space R3 with the regular addition, and scalar aL multiplication. Is The set of all vectors of the form b, subspace of R3 Question (9) a) Let S- {2-x + 3x2, x +...
Question (7) Consider the vector space R3 with the regular addition, and scalar aL multiplication. Is The set of all vectors of the form b, subspace of R3 Question (9) a) Let S- {2-x + 3x2, x + x, 1-2x2} be a subset of P2, Is s is abasis for P2? 2 1 3 0 uestion (6) Let A=12 1 a) Compute the determinant of the matrix A via reduction to triangular form. (perform elementary row operations)
Question (7) Consider...
Let E be the plane in R3 spanned by the orthogonal vectors v1=(121)and v2=(−11−1) The reflection...
Let E be the plane in R3 spanned by the orthogonal vectors v1=(121)and v2=(−11−1) The reflection across E is the linear transformation R:R3→R3 defined by the formula R(x) = 2 projE(x)−x (a) Compute R(x) for x=(1260) (b) Find the eigenspace of R corresponding to the eigenvalue 1. That is, find the set of all vectors x for which R(x) =x. Justify your answer.
An) a) Find the magnitude of both vectors. b) Find dot product and cross product of both vectors ...
pls answer 4,5,6 and 7
An) a) Find the magnitude of both vectors. b) Find dot product and cross product of both vectors c) Find the projection of w onto v 2) Let а:31 + 5, + 7k and b--6r +-10, + mk where m e R. a) Find the value for m such that vectors are orthogonal b) Find the value of m such that the cross product of the vectors is zero 3) a) Find the distance from...
1. Given the following 3 vectors, evaluate a. 2A+B b. C-A c. 2BXC-omit d. C-(AXB) -...
1. Given the following 3 vectors, evaluate a. 2A+B b. C-A c. 2BXC-omit d. C-(AXB) - Ort A = 2i - 13 + 4k B=4i + ij - 5k C = -2i+2j – 3k = 120 at 450 - 200 at 1260 Find D E 2. The position of an object is related to time by X = Ata--Bt + C, where A -6m/s?.
Question 2 {(1,-,,,1)} and C {(1,-,0), 0, 0,1)} be subsets of R3 Let B (a) Show...
Question 2 {(1,-,,,1)} and C {(1,-,0), 0, 0,1)} be subsets of R3 Let B (a) Show that both the sets B and C are lhnearly independent sets of vectors with spanB = spanC 12 marks (b) Assuming the usual left to rıght orderıng, find the transıtion matrıx PB-C [2 marks (c) Given a basıs D of R, find the transıtion matrıx PBD given 2 1 3 2 Pc-D 3 marks (c) to find D (d) Use the transıtion matrıx PcD...
(4) Let F be a field and let a, b E F with a 0. Show that Fx/axb)F
(4) Let F be a field and let a, b E F with a 0. Show that Fx/axb)F
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...
b) Let a R3 be a vector of length 1. Define H={x E R3 : a·x=0). Here a x denotes the dot product of the vectors a and x. (i) Show that H is a subgroup of R (ii) For λ E R, show that : a·x= is a coset of H in R3. (ii) Is H cyclic? Prove or disprove.
b) Let a R3 be a vector of length 1. Define H={x E R3 : a·x=0). Here a x...
2 5 Do the vectors u = and v= 3 7 span R3? -1 1 Explain! Hint: Use Let a, a2,ap be vectors in R", let A = [a1a2..ap The following statements are equivalent. 1. ai,a2,..,a, span R" = # of rows of A. 2. A has a pivot position in every row, that is, rank(A) Select one: Oa. No since rank([uv]) < 2 3=# of rows of the matrix [uv b.Yes since rank([uv]) =2 = # of columns of...
Let S be the tetrahedron in R3 with vertices at x the vectors 0, e1, e2, and e3, and let S' be the tetrahedron with vertices at vectors 0, v1, V2 and v3. See the figures to the right. Complete parts (a) and (b) below. a. Describe a linear transformation that maps S onto S lf T is a linear transformation that maps S onto S, then the standard matrix for T, written in terms of v1-v2, and v3, is...
Question (7) Consider the vector space R3 with the regular addition, and scalar aL multiplication. Is The set of all vectors of the form b, subspace of R3 Question (9) a) Let S- {2-x + 3x2, x + x, 1-2x2} be a subset of P2, Is s is abasis for P2? 2 1 3 0 uestion (6) Let A=12 1 a) Compute the determinant of the matrix A via reduction to triangular form. (perform elementary row operations)
Question (7) Consider...
pls answer 4,5,6 and 7
An) a) Find the magnitude of both vectors. b) Find dot product and cross product of both vectors c) Find the projection of w onto v 2) Let а:31 + 5, + 7k and b--6r +-10, + mk where m e R. a) Find the value for m such that vectors are orthogonal b) Find the value of m such that the cross product of the vectors is zero 3) a) Find the distance from...
1. Given the following 3 vectors, evaluate a. 2A+B b. C-A c. 2BXC-omit d. C-(AXB) - Ort A = 2i - 13 + 4k B=4i + ij - 5k C = -2i+2j – 3k = 120 at 450 - 200 at 1260 Find D E 2. The position of an object is related to time by X = Ata--Bt + C, where A -6m/s?.
Question 2 {(1,-,,,1)} and C {(1,-,0), 0, 0,1)} be subsets of R3 Let B (a) Show that both the sets B and C are lhnearly independent sets of vectors with spanB = spanC 12 marks (b) Assuming the usual left to rıght orderıng, find the transıtion matrıx PB-C [2 marks (c) Given a basıs D of R, find the transıtion matrıx PBD given 2 1 3 2 Pc-D 3 marks (c) to find D (d) Use the transıtion matrıx PcD...
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