1. Given the vectors and matrices defined below Tol u= 1 ; w= 1 1-1] [3...
3) Let u a) Treating u, v', and w' as vectors, are the inner products u.v', v'.u, and u.w' defined? If yes, compute them. If any of them is not defined, explain why not. b) Treating u, v', and ' as matrices, are the products uv', v'u, and w' defined? If yes, compute them. If any of them is not defined, explain why not.
Need help!! 1) Let A, B, C, and D be the matrices defined below. Compute the matrix expressions when they are defined; if an expression is undefined, explain why. [2 0-1] [7 -5 A= .B -5 -4 1 C- ,D= (-5 3] [I -3 a) AB b) CD c) DB d) 3C-D e) A+ 2B 2) Let A and B be the matrices defined below. 4 -2 3) A=-3 0, B= 3 5 a) Compute AB using the definition of...
it veetors délfhed above 2) Find the length of vector i-2 3 s 3) Let u--3 v 3 2l, and w [5 -1l 2 a) Treating u, v', and w, as vectors, are the inner products uw, v,u, and 1.w, defined? If yes, compute them. If any of them is not defined, explain why not. b) Treating u,v, and w' as matrices, are the products n', p'u and zm defined? If yes, compute them. If any of them is not...
41 and w be vectors, and 39-42 Properties of Vectors Let u, V, and w be ved let c be a scalar. Prove the given property. 39. u. v = v.u 40. (cu) v = c(u.v) = u • (cv) 41. (u + v). w = uw + v.w 42. (u - v)•(u + v) = | u |2 - 1 v 12
Please solve using matrices and not equations. Thanks. 2. Given the columns of the matrix u v w 0 1 2 0-1 0 0 r S t -1 021 01 0 For each of the sets of vectors given below, answer the following questions: (i) Is the set linearly independent? 1 Does the set span (iii Does the vector a- (a) S (r, s, t, u) (b) T fr,t, 0, u) (c) U = {r, t, w, u, v} (3,2,1,5)...
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=
Given matrices 3 4 and B 5-17 4 3 8 and vectorS compute the matrix AB and the vectors Verify that the columns of AB are given by AVM, AV2, AVs, respectively
7. The set {u, v, w} is an orthogonal set of vectors, where u= (0,3,4), v = (1,0,0) and w = (0,4, -3). If (0,-1,-1) = au + bu + cw, then (a, b, c) = mark (x) the correct answer: A (-3,0,-) B (-2, 0, - 2) C (7,0, ) D(-2,0, 35) E (-7,0, -1) F (0,-1, -1)
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)...
composition of two functions Suppose that the functions u and w are defined as follows. u(x)=-4x-2 w(x) = -5x+1 Find the following. (uw)(-4) = 0 0/6 (wu)(-4) = Х 5 ?