Find (u, v), ||u|l, ||v||, and d(u, v) for the given inner product defined on R". u = (-4, 0), v = (3, -5), (u, v) = 3u1V1 + uzv2 (a) (u, v) (b) ||u|| (c) ||v||

Q: 7. Is this a linearly independent subset of R³ ? {(1, 4, −6), (1, 5, 8), (2, 1, 1), (0, 1, 0)}…

A:

Q: 10. Let n > 2 be an integer and let V be the subset of F" consisting of vectors (x1,..., xn)…

A:

Q: Show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2,…

A: We have to show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v…

Q: Let u =(5,5,0) and v=(,5,5,(5sqrt2). Compute |u*v|

A: Approach to solving the question: Detailed explanation: Examples: Key…

Q: u = 3i – 2 j+4k v=i-3j-k 18) (Section 9.7) Find the cross product in space i j KI 3 -2 4 -3 -1|

A:

Q: Show that λis a root of char(x) if and only if there exosts a non-zero vector v in V with L(v)=λv

A: Assume that λ is a root of charL(x) then | λIdv–L | = 0. It is known that, the system of Bx = 0 has…

Q: (a) Use determinants to compute the area of the parallel- ogram spanned by the vectors (2, 3) and…

A: Note the results : Suppose we have two vectors u=<u1,u2> and v=<v1,v2> .Then area of…

Q: State why (u,v) =u,³v,² +u₂³v₂² is not an inner product for u = (u,,u,) and v= (v₁,v₂) in R².

A:

Q: Given the vector (x <- c(5, 2, 7), what would x^2 return? O [1] 78 O [1] 196 O [1] 25 4 49 O [1] 10…

A: Given that, the vector is        ,we need to find .

Q: Use Green's theorem to find $ x? ydr + xdy over a counterclockwise triangular path passing though…

A: To find the line integral ∮x2ydx+xdy by using Green's theorem, First, we need to draw the given…

Q: Find the norm of the projection of u onto a ( || proj,u || ) with the following: (a) u=(1, – 2). a…

A:

Q: True or False: (p, q) = p(1)q(1)+p(2)q(2) +p(3)q(3) defines an inner product on P2(R).

A:

Q: 6. Show that each of the following are not inner products on R³, (a) (u, v) = U₁V₁ + U2V2; (b) (u,…

A:

Q: If are arbitrary vectors in R2x2, then the mapping A = (A, B) || A|| = ||B| = [a11 a12] a21 a22 A =…

A:

Q: Show that u and v are orthogonal if and only if ||u+v|| 2 = ||u|| 2 + ||v|| 2

A:

Q: Use the inner product (A,B) = 2a11b11 + a21b21 + a12b12 + 2a22b22 to find (A, B) for 0 A - [27][221]…

A: Given A = 1-124,   B = 01-20

Q: Consider an inner product on two P3 vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(1)g(1) + f(2)g(2):…

A: Since you have posted multiple subpart question, we will solve the first three sub parts for you. If…

Q: Show that there do not exist scalars c₁, c₂, and C3 such that c₁(1,0, 1,0) + c2 (1, 0, 2, 1) +…

A:

Q: Compute the dot product (7, 6, 8) - (4, 10, 8).

A: To find - Compute the dot product 7, 6, 8·4, 10, 8

Q: (-4,2+i, 1), and y = (i, 5, 1 + i) be vectors in C. Compute (r, y), Let z = ||x||, ||y||, and ||r+…

A: