13) For the vectors u = (7,3) and w=(-4,6) find all of the following a) 2u...
Let w be a subspace of R", and let wt be the set of all vectors orthogonal to W. Show that wt is a subspace of R" using the following steps. a. Take z in wt, and let u represent any element of W. Then zu u = 0. Take any scalar c and show that cz is orthogonal to u. (Since u was an arbitrary element of W, this will show that cz is in wt.) b. Take z,...
(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
3. (6 marks) Suppose that u, v and w are vectors in R3, and that u. (v x w) = 3. Determine (a) u (w x v) (b) u: (w X w) (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
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)...
0/1 pts Inooreat Question 9 Suppose W is a subspace of R" spanned by n nonzero orthogonal vectors. Explain why WR Two subspaces are the same when one subspace is a subset of the other subspace. Two subspaces are the same when they are spanned by the same vectors Two subspaces are the same when they are subsets of the same space Two subspaces are the same when they have the same dimension Incorrect 0/1 pts Question 10 Let U...
Problem 13. For each of the following we are given two vectors u, we V and a linear trans- formation from a vector space V to itself. Check if the given vectors are eigenvectors for the transformation. If yes, then find the corresponding eigenvalues. (a). V=P3, 7(p(x))=x?p"(x) — xp'(x), with u =2+3x? and w=x?. (b). V = Muj, T(A)=A+A”, with u=[?) and w=[; ?] (c). V = P2, L(P(x) p(x)dx + (x – 3)p'(x) with u = 100 and w=3+3x.
1- Two vectors are given as u = 2 – 5j and v=-{+3j. a- Find the vector 2u +3v (by calculation, not by drawing). (4 pts) b- Find the magnitudes luand il of the two vectors. (4 pts) c- Calculate the scalar product u•v. (5 pts) d- Find the angle between the vectors u and v. (6 pts) - Calculate the vector product uxv. (6 pts)
Caculate w=2U+V, |U|,|V| and |W| A= <1,-3,7> and B=<-5,2,-3> Find C sp A+B+C=0
1- Two vectors are given as u = 2î – 5j and v=-î +3j. a- Find the vector 2u + 3v (by calculation, not by drawing). (4 pts) b- Find the magnitudes lil and 17% of the two vectors. (4 pts) c- Calculate the scalar product uov. (5 pts) d- Find the angle 0 between the vectors ū and . (6 pts) e-Calculate the vector product u xv. (6 pts)