Let W be a subspace of R", and let W- be the set of all vectors orthogonal to W. Show that W- is a subspace of R" using the following steps. a. Take z in W+, and let u represent any element of W. Then z•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 W-.) b. Take z1 and z2 in W+, and let u be any element of W. Show that zi + z2 is orthogonal to u. What can you conclude about z¡ + z2? Why? c. Finish the proof that W- is a subspace of R".

Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A: Given W be a subspace spanned by the u's, We have to write y as the sum of a vector in W and a…

Q: Is the set of all vectors (x, y) in R, with the usual addition and scalar multiplication, a subspace…

A:

Q: Let V=R². For (u₁, U₂), (v₁, v₂) € V and a € R define vector addition by (u₁, ₂) (V₁, V₂) = (U₁ +…

A: The given vector space is .For any  and , the vector addition and scalar multiplications are defined…

Q: Let L be the line in R³ that consists of all scalar multiples of the vector onto L. proje 22 T .…

A:

Q: 2. Determine whether the following sets with the corresponding vector addi- tion and scalar…

A:

Q: Consider the vector v = (6, 1, -3) in R. Let V be the subspace of R consisting of all vectors of the…

A:

Q: Give a contrapositive proof of the following: If n is an odd integer, then the equation x2+ x -n=0…

A:

Q: W4 Pick any vector space V that you want, as long as dim(V) ≥ 6. Then, pick 4 vectors in the space,…

A:

Q: If A is m X n, prove that every vector in null(A) is orthogonal to every vector in row(A).

A: Let A be an m×n matrix. We want to prove that every vector in the null space of A is orthogonal to…

Q: Suppose that f is a vector of length 8 with F1{feven} = -2 – i and F{f»dd} = 3+i. %3D Compute the…

A:

Q: Determine whether W is a subspace of V

A: Determine whether W is a subspace of V

Q: Let the set U = b:c = a = R3 be given. Then which of the following statement or statements are…

A:

Q: Q1. If O (0,0,0) in (x,y,z) 3-D space and r(2,5,1) draw the vector in 3D and find its direction.

A: Plot point in 3D

Q: Let V = R2, defined the addition by: (u1 tu2) + (v1 + vz)=( U1 +v1 , Uz tv2 + 1) With standard…

A: Given that the vector addition on V=ℝ2 is defined by           u1,u2+v1,v2=u1+v1,u2+v2+1 with…

Q: Show that the set T= {(a, b, c, d): 2a-3b+Sc-d=0} is a subspace of R'.

A: Given T=abcd∈ℝ4:2a-3b+5c-d=0 Let A be a 1×4 matrix defined by: A=2-35-1 Then the equation…

Q: Find the new coordinate vector for the vector x after performing the specified change of basis. 10)…

A:

Q: Suppose U and W are subspaces of a vector space V. Prove that if U C W, then U + W = W.

A:

Q: Suppose U and W are two-dimensional subspaces of R3. Show that U∩W≠{0}

A: We want to show that  U∩W≠{0}

Q: Let x and y be two orthogonal vectors. Then prove that +

A:

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

A:

Q: 1. Let v, = (43 2 1), v, = (-2 0 -1 0), v3 = (0 3 0 1) a) Find the subspace of R* spanned by these…

A:

Q: Let V = R' and define vector addition as (x, y, z)+(x', y', z')= (x+x',y+y',z+z') (standard…

A:

Q: Let V = Row,, the vector space of 2-dimensional row vectors. Let B be the following basis for V. B =…

A:

Q: Let V=R\power{3}. Show the set    W={(a,b,c): a\power{2

A: Our claim is that given subset W of V=R3 is not a subspace of V.Where   W=(a,b,c): a2+b2+c2≤1

Q: Find the vecctor projection of u=bi+3jtak onto Vzi-zj-2k and the scalar component of u in the…

A:

Q: If W is a subspace of R" and if u is in both W and w then u must be a zero vector.

A: I am going to solve the given problem by using the orthogonal property of a vector.