Linear Algebra Question:
![:]suchthata,b,c,dso 6. 18 Points] Show that V, the set of all 2x2 matrices of the form such that a, b, c, d s0, is not a subs](http://img.homeworklib.com/images/149cbd86-0cad-479b-8c87-6e87fd8460d6.png?x-oss-process=image/resize,w_560)
![s. I5 Points each] Let ü = (2,-6, 2), v = (0, 4,-2), and w-(2, 2,-4) a. Find a vector that is orthogonal to both v and w usin](http://img.homeworklib.com/images/3150c402-a83c-4036-9d06-d67a07c36938.png?x-oss-process=image/resize,w_560)
Forgot to include the vaules of u, v and w.
s. I5 Points each] Let ü = (2,-6, 2), v = (0, 4,-2), and w-(2, 2,-4) a. Find a vector that is orthogonal to both v and w using the cross product. b. Find the area of the parallelogram in R determined by v and w.
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Linear Algebra Question: Forgot to include the vaules of u, v and w.
Exercise Set Chapter 3 Q1) Let u = (2, -2, 3), v = (1, -3, 4),...
Exercise Set Chapter 3 Q1) Let u = (2, -2, 3), v = (1, -3, 4), and w=(3,6,-4). a) Evaluate the given expression u + v V - 3u ||u – v| u. V lju – v|w V X W ux (v x W) b) Find the angle 8 between the vector u = (2,-2,3) and v = (1, -3,4). c) Calculate the area of the parallelogram determined by the vector u and v d) Calculate the scalar triple product...
-9 2. Let Vi-8.V2,andvs-2, let B -(V,V2,Vs), and let W be the subspace spanned , let B -(Vi,V2,V3...
-9 2. Let Vi-8.V2,andvs-2, let B -(V,V2,Vs), and let W be the subspace spanned , let B -(Vi,V2,V3), and let W be the subspace spanned by B. Note that B is an orthogonal set. 17 a. 1 point] Find the coordinates of uwith respect to B, without inverting any matrices or L-2 solving any systems of linear equations. 35 16 25 b. 1 point Find the orthogonal projection of to W, without inverting any matrices or solving any systems of...
slove fast plz 6) [15 marks] Let V be the vector space of all 2x2 matrices...
slove fast plz
6) [15 marks] Let V be the vector space of all 2x2 matrices over R. Let W, be the subspace consisting of matrices A such that , + Ay = 0, and W, be the subspace consisting of all matrices B such that B2+ Bx = 0. i. [5 marks] Find a basis for W; ii. (5 marks] Find a basis for W,; iii. [5 marks] Find dimW,, dimW,, dim(W+W,) and dim(W, nw).
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=
5/9/2019 the closest point to y in the subspace W spanned by u, and u Let...
5/9/2019 the closest point to y in the subspace W spanned by u, and u Let W be the subspace spanned by 11. and u2. Write y as the sum of a vector in W and a vector orthogonal to w u, 12 13)- 12 25 3 5 6-5 | and b = | 4 l. Describe the general solution in parametric Describe all solutions of Ax = b, where A-1-2 -4 7 0 vector form
8. If ü= 8i - 15j and = -31 - 4; and w = 121 +...
8. If ü= 8i - 15j and = -31 - 4; and w = 121 + 6j, then find the following: A. 2w - 3ü B. ||2u - 501 C. J. D. the angle between ü and v E. the direction angle of vector w F. (3x + 70). a vector in the same direction as u with magnitude of 12 a vector orthogonal to vector V with magnitude of 7 any vector that is orthogonal to the vector w...
8. If ū= 8î - 159 and v = -3i - 4ſ and w = 12...
8. If ū= 8î - 159 and v = -3i - 4ſ and w = 12 + 69, then find the following: A. 2w - 3ū B. ||2u - 57 C. v. W D. the angle between ü and v E. the direction angle of vector w F. (3 +70).ü G. a vector in the same direction as ū with magnitude of 12 H. a vector orthogonal to vector v with magnitude of 7 I. any vector that is orthogonal...
please anyone answer all the questions as soon please 2 4 3 3 4 1. Given...
please anyone answer all the questions as soon please
2 4 3 3 4 1. Given three points A = (0,–8, 10), B = (2, -5, 11), C = (-4,-9, 7) in R3. (a) Show that these three points are not collinear (not in a straight line). (b) Find the area of the triangle ABC. (c) Find the scalar equation of the plane containing the points A, B and C. (d) Find a point D on the plane such that...
1 Problem 4. Let V be a vector space and let U and W be two subspaces of V. Let (1) Prove that ifU W andWgU then UUW is not a subspace of V (2) Give an example of V, U and W such that U W andWgU. Expl...
1
Problem 4. Let V be a vector space and let U and W be two subspaces of V. Let (1) Prove that ifU W andWgU then UUW is not a subspace of V (2) Give an example of V, U and W such that U W andWgU. Explicitly verify the implication of the statement in part1). (3) Proue that UUW is a subspace of V if and only if U-W or W- (4) Give an example that proues the...
1. Let u - (1,1,2), v = (1,2,1), and w (2,1,1) in R. and consider •...
1. Let u - (1,1,2), v = (1,2,1), and w (2,1,1) in R. and consider • the parallelogram B = {s(3v) + t-w) 0 <s,t<1, s,te R} spanned/formed by the vectors (3v) and (-w), and • the parallelepiped P = {ru + s(3v) + (-w) 0 <T,,t<1, r, s, t€ R} [10] spanned formed by vectors u. (3v). and (-w) We take the parallelogram B as a base of P. (a) Does the ordered vector triple (v xw, 3v, -w),...
Exercise Set Chapter 3 Q1) Let u = (2, -2, 3), v = (1, -3, 4), and w=(3,6,-4). a) Evaluate the given expression u + v V - 3u ||u – v| u. V lju – v|w V X W ux (v x W) b) Find the angle 8 between the vector u = (2,-2,3) and v = (1, -3,4). c) Calculate the area of the parallelogram determined by the vector u and v d) Calculate the scalar triple product...
-9 2. Let Vi-8.V2,andvs-2, let B -(V,V2,Vs), and let W be the subspace spanned , let B -(Vi,V2,V3), and let W be the subspace spanned by B. Note that B is an orthogonal set. 17 a. 1 point] Find the coordinates of uwith respect to B, without inverting any matrices or L-2 solving any systems of linear equations. 35 16 25 b. 1 point Find the orthogonal projection of to W, without inverting any matrices or solving any systems of...
slove fast plz
6) [15 marks] Let V be the vector space of all 2x2 matrices over R. Let W, be the subspace consisting of matrices A such that , + Ay = 0, and W, be the subspace consisting of all matrices B such that B2+ Bx = 0. i. [5 marks] Find a basis for W; ii. (5 marks] Find a basis for W,; iii. [5 marks] Find dimW,, dimW,, dim(W+W,) and dim(W, nw).
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=
5/9/2019 the closest point to y in the subspace W spanned by u, and u Let W be the subspace spanned by 11. and u2. Write y as the sum of a vector in W and a vector orthogonal to w u, 12 13)- 12 25 3 5 6-5 | and b = | 4 l. Describe the general solution in parametric Describe all solutions of Ax = b, where A-1-2 -4 7 0 vector form
8. If ü= 8i - 15j and = -31 - 4; and w = 121 + 6j, then find the following: A. 2w - 3ü B. ||2u - 501 C. J. D. the angle between ü and v E. the direction angle of vector w F. (3x + 70). a vector in the same direction as u with magnitude of 12 a vector orthogonal to vector V with magnitude of 7 any vector that is orthogonal to the vector w...
8. If ū= 8î - 159 and v = -3i - 4ſ and w = 12 + 69, then find the following: A. 2w - 3ū B. ||2u - 57 C. v. W D. the angle between ü and v E. the direction angle of vector w F. (3 +70).ü G. a vector in the same direction as ū with magnitude of 12 H. a vector orthogonal to vector v with magnitude of 7 I. any vector that is orthogonal...
please anyone answer all the questions as soon please
2 4 3 3 4 1. Given three points A = (0,–8, 10), B = (2, -5, 11), C = (-4,-9, 7) in R3. (a) Show that these three points are not collinear (not in a straight line). (b) Find the area of the triangle ABC. (c) Find the scalar equation of the plane containing the points A, B and C. (d) Find a point D on the plane such that...
1
Problem 4. Let V be a vector space and let U and W be two subspaces of V. Let (1) Prove that ifU W andWgU then UUW is not a subspace of V (2) Give an example of V, U and W such that U W andWgU. Explicitly verify the implication of the statement in part1). (3) Proue that UUW is a subspace of V if and only if U-W or W- (4) Give an example that proues the...
1. Let u - (1,1,2), v = (1,2,1), and w (2,1,1) in R. and consider • the parallelogram B = {s(3v) + t-w) 0 <s,t<1, s,te R} spanned/formed by the vectors (3v) and (-w), and • the parallelepiped P = {ru + s(3v) + (-w) 0 <T,,t<1, r, s, t€ R} [10] spanned formed by vectors u. (3v). and (-w) We take the parallelogram B as a base of P. (a) Does the ordered vector triple (v xw, 3v, -w),...
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