3. (6 marks) Suppose that u, v and w are vectors in R3, and that u....
(6 marks) Suppose that u, v and w are vectors in R3, and that u. (v x w) = 3. Determine (a) u (w xv) (b) u. (w xw) (c) (2u x v). w
(6 marks) Suppose that u, v and w are vectors in R 3 , and that u · (v × w) = 3. Determine 3. (6 marks) Suppose that u, v and w are vectors in R3, and that u. (vx w) = 3. Determine (a) u (w xv) (b) u (w xw) (c) (2u xv).w
linear alegbra Let u, v, w be linearly independent vectors in R3. Which statement is false? (A) The vector u+v+2w is in span(u + u, w). (B) The zero vector is in span(u, v, w) (C) The vectors u, v, w span R3. (D) The vector w is in span(u, v).
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)...
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...
Problem #7: Which of the following statements are always true for vectors in R3? (i) If u (vx w)-4 then w - (vxu)-4 (ii) (5u + v) x (1-40 =-21 (u x v) (ili) If u is orthogonal to v and w then u is also orthogonal to w | V + V W (A)( only (B) (iii) only (C) none of them (D) (i) and (iii) only (E) all of them (F) (i) only (G)i and (ii) only (H)...
(22). (10 Marks). Consider vectors v = 0 - in R3 (a). (5 marks) Find a basis of the subspace of R3 consisting of all vectors perpendicular to v. (b). (5 marks) Find an orthonormal basis of this subspace.
Question 25 Use the vectors in the figure belo w u * Z v 11 2u - Z-W
Question 6) (9 points) Prove each of the following statements. (a) Suppose that the vectors {v, w, u} are linearly independent vectors in some vector space V. Prove then that the vectors {v + w, w + u,v + u} are also linearly independent in V. (b) Suppose T is a linear transformation, T: P10(R) → M3(R) Prove that T cannot be 1-to-1 (c) Prove that in ANY inner product that if u and w are unit vectors (ie ||vl|...
[3] Given: u = -8i + 6 v = i- j w = 4i - 8j T = -10i Point Pat (-17, -v2), point at (-9, 11), and point Rat (8, -15) Five of the following six parts are each worth 3 points. Part b is worth 5 points. a) Find the position vector, in xi + yj form, for the vector whose initial point is R and whose terminal point is 9. b) Sketch the position vector determined by...