2. The subspace (a) 2y x+y+z=0 1 in R3 is a plane whose equation is x-2=0 (b) y (c). x-2y+z=0 Py27. y-z=o
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- Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector u=(1,1,1,1) in the form u=v+w, where v is in V and w is orthogonal to every vector in V.Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}Find the orthogonal trajectories of the conicoid (x + y)z = 1 of the conics in which it is cut by the system of the plane x − y + z = K where K is a parameters
- Let V = { [x y z] in ℝ^3 ∶ z = 2x - y }. Is V a subspace of ℝ^3? If it is, what is the dimension of V? Any help (especially with details) would be greatly appreciated.In V=R3 Let W1 be the xy-plane and let W2 be the z-zxis: W1={(x,y,0):x,y∈R} and W2={(0,0,z):z∈R} Show thatFind a basis for the subspace given by the plane −3x + 2y + 5z = 0.
- What is the dimension of the sum of subspaces V and W in R3[x], where V={f∈R3[x]∣ f(0)=0} and W=span{x}? (a) 0.(b) 1.(c) 2.(d) 3.(e) 4.Let S=span(e1), T=span(e2) and W=span(e1+e3) be subspaces of R3. S is orthogonal to T, T is orthogonal to W, then S is orthogonal to W. true or false?if v is in R3, does the set of vectors x with v x x=0 is a subspace?
- Find the projection of the vector v = [1 0 −2]T onto the subspaceLet W = {(x, y, z) : x = 2y and x, y, z ∈ F} of F3 be a subspace. How can I prove that F2 and W are isomorphic?Compute the vector assigned to the pointP = (−3, 5) by the vectorfield:(a) F(x, y) = (xy,y − x)(b) F(x, y) = (4, 8)(c) F(x, y) = 3x+y , log2(x + y)