Let v=(1,-4,12) and w=(3,5,-1) be vectors.
What is 2v-3w?
Given v=(1,-4,12) and w=(3,5,-1) 2v = (2, -8, 24) 3w = (9, 15, -3) 2v-3w = (2-9 -8-15 24+3) = (-7 -23 27)
(-7 -23 27)
use the vectors v=-2i + j and w=4i -3j to find the following 4v – 3w .
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 >
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
Let v and w be vectors in an inner product space V. Show that v is orthogonal to w if and only if ||v + w|| = ||v – w||.
Let v and w be two vectors whose modules are equal to 3 and 1, respectively the angle formed between them is equal to π / 6. If θ denotes the measure of the angle between v + w and v-w, how much is cos θ worth?
5. Let ū and w be vectors in R3. Prove that (ö - w) x (v + 2) = 2(vx w).
Use the given vectors to compute u + v, u - v, and 5u - 2v. u = (9,-3), v = (1,7) U + V = U - V = 5u - 2y =
Question 1 Question 2 Let u, v, w be three vectors in R4 with the property that 4u - 30+2w = 0. Let A be the 4 x 2 matrix whose columns are u and u (in that order). Find a solution to the equation Ac =W. Let 1 -2 0 3 A=1 -2 2-1 2 -4 1 4 Find a list of vectors whose span is the set of solutions to Ax = 0. 1 1 Enter the list...
Let V be an inner product space and u, w be fixed vectors in V . Show that T v = <v, u>w defines a linear operator in V . Show that T has an adjoint, and describe T ∗ explicitly
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=