Let u = [5,0,-1], v = [0,-6,2] and w = [5,6,-1] Find the values c, y,...
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be the line in R3 that passes through the point P and is perpendicular to both of the vectors v and w. Find an equation for the line L in vector form. (iii) Find parametric equations for the line L.
[1] In parallelogram WXYZ, if u joins X to Y and v joins X to W, which connection forms a vector equal to u + v? v + u? u-v? V-u? A. W to Y B. Y to W C. X to Z D. Z to X W z Y [2] A linear combination of vectors is given. Determine the resultant vector using the tip- to-tail method for adding vectors geometrically. (9,-6) + (-12, -1) - (3, -15) + 5(2,...
Let V be the set of vectors shown below. V= Ox>0, y>0 a. If u and v are in V, is u + v in V? Why? b. Find a specific vector u in V and a specific scalar c such that cu is not in V. a. If u and v are in Vis u + vin V? O A. The vector u + v must be in V because V is a subset of the vector space R2...
Let V be the set of vectors shown below. V= [] :x>0, y>0 a. If u and v are in V, is u + v in V? Why? b. Find a specific vector u in V and a specific scalar c such that cu is not in V. O A. The vector u + v may or may not be in V depending on the values of x and y. OB. The vector u + y must be in V...
Let A-g's, u, v, w, x, y, z), B {q, s, y, z,C-{v, w, x, y, z), and D-6. Specify the following set. 9) Cu B 10) An B
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=
Question 2 Let U = {q, r, s, t, u, v, w, x, y, z} C = {v, w, x, y, z}. List the elements in the set. CU
1 3. Consider the vector v= (-1) in R3. Let U = {w € R3 :w.v=0}, where w.v is the dot product. 2 (a) Prove that U is a subspace of R3. (b) Find a basis for U and compute its dimension. 4. Decide whether or not the following subsets of vector spaces are linearly independent. If they are, prove it. If they aren't, write one as a linear combination of the others. (a) The subset {0 0 0 of...
Let A be an m × n matrix, let x Rn and let 0 be the zero vector in Rm. (a) Let u, v є Rn be any two solutions of Ax 0, and let c E R. Use the properties of matrix-vector multiplication to show that u+v and cu are also solutions of Ax O. (b) Extend the result of (a) to show that the linear combination cu + dv is a solution of Ax 0 for any c,d...
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...