2 ---- Let y = 8 = 1 a. Let U = = [₁ u₁ u₂ UTU= 10 01 23 13 and UUT = - 680 ]. Compute UTU and UUT. 23 13 23 6|N 8 2 6N 9 9 b. Compute projwy and (UUT) y. projwy = and (UUT) y = 24 and W= Span {u₁,u₂}. Complete parts (a) and (b). 25 4 99 9 9 9 - 2 9 59 (Simplify your answers.) (Simplify your answers.)

Q: Let →a=a→= and →b=b→=. Find kk so that →aa→ and →bb→ will be orthogonal (form a 90 degree angle).…

A: We Know that, Two vectors u and v are said to be orthogonal vectors if and only if u . v=0 Here, a =…

Q: 6. Find UV (dot a) Ū · V = (2, 3, -

A:

Q: 4. For what value of h is vz in Span {v, v2} and for what value of h is {v1, V2, V3} linearly…

A: v1=1-32, v2=-39-6 and v3=5-7h

Q: 8. If it [13,7.-2] is orthogonal to v v=[-5, k.7], determine the value(s) of k.

A: Given query is to find the value of k.n

Q: Let L be the line passing through the point P(-1, -3, -2) with direction vector d=[-1, 1, 1]T. Find…

A:

Q: Let u = (3, 2, x) and v = (2x, 4, x). (a) Find all possible values of x that make u and v…

A: Given thata)We have to find all possible values of x that make u and v orthogonal.b)We have to find…

Q: Find the projection of u = onto v = .

A:

Q: Let u = 4 h = V= and w= 1 . For what value of h is w in the plane spanned by u am

A:

Q: Let a = (5, 4) and b = (5, – 8). Compute the dot product. a b

A:

Q: Compute the orthogonal projection of u onto v. Use the square root symbol '' where needed to give an…

A:

Q: 9. Let A=span{v = (-1,–1,2), i = Projau. (2,3,0)} and w (1,2, 3). Find

A:

Q: Find the distance from P(1, -2, 3) to Q(-3, 5, -2).

A:

Q: Let a = (3, −4, 9) (a) Find k such that b = (−2, k, −6) is parallel to a. (b) Find k such that b =…

A:

Q: Use v=<3/5, 4/5>, w= <-4/5, 3/5> to find v.w and proj w(v)

A: Given thatv = <3/5, 4/5> and w = <-4/5, 3/5>To find:wprojwV