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Linear algebra question Let u=(1-2-1) and v=(2,-1,-2). What is the value of the constant c such...
This is an advanced linear question on linear algebra. Please answer as soon as possible. 3. (15 points) Let L denote the line in the plane consisting of all scalar multiples of the veto hat is the matrix that represents the orthogonal projection of R2 onto the line L
For parts ( a ) − ( c ), let u = 〈 2 , 4 , − 1 〉 and v = 〈 4 , − 2 , 1 〉. ( a ) Find a unit vector which is orthogonal to both u and v. ( b ) Find the vector projection of u onto v. ( c ) Find the scalar projection of u onto v.
Q2 - Linear Algebra - Fundamental Subspaces, linear mappings, etc Let U, V, and W be vector spaces. Verify that if L :V → W and M : W →U are both linear mappings, then so is the composition MoL:V → U. Moreover, prove that if L and M are both invertible linear mappings, then so is Mo L.
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 >
Question 19: Linear Transformations Let S = {(u, v): 0 <u<1,0 <v<1} be the unit square and let RCR be the parallelogram with vertices (0,0), (2, 2), (3,-1), (5,1). a. Find a linear transformation T:R2 + R2 such that T(S) = R and T(1,0) = (2, 2). What is T(0, 1)? T(0,1): 2= y= b. Use the change of variables theorem to fill in the appropriate information: 1(4,)dA= S. ° Sºf(T(u, v)|Jac(T)| dudv JA JO A= c. If f(x, y)...
This is a question for Advanced Linear Algebra. Please answer ALL parts well and completely, and please write CLEARLY, with neat, non-cursive writing. Make sure x's and v's and y's, s's and such are clearly different. I sometimes have trouble reading the difference with people's handwriting. Thank you, thumbs up if you can! (1) $5.9, Let X, be subspaces of R3 with bases given respectively by (a) Show that and are complementary. (b) Find the projector P onto X along...
I need the answer to problem 6 Clear and step by step please Problem 4. Let V be a vector space and let T : V → V and U : V → V be two linear transforinations 1. Show that. TU is also a linear transformation. 2. Show that aT is a linear transformation for any scalar a. 3. Suppose that T is invertible. Show that T-1 is also a linear transformation. Problem 5. Let T : R3 →...
Recall from linear algebra the definition of the projection of one vector onto another. As before, we have 3-dimensional vectors = a2 a3 and (2) -a2 - a3 What is the signed magnitude c of the projection pf)-r2) of x1) onto a(2)? More precisely, let u be the unit vector in the direction of the correct choice above, find a number c such that pri)-g(2) == CU. Express your answer in terms of a 1 for a1, a_2 for a2,...
Linear Algebra Question: Forgot to include the vaules of u, v and w. :]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 subspace. 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...
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...