question below:

x Let H = : 8x2 + 4y2 $1 , which represents the set of points on and inside an ellipse in the xy-plane. Find two Y specic examplestwo vectors, and a vector and a scalarto show that H is not a subspace of R2. H is not a subspace of [R2 because the two vectors D show that H |::l closed under Z (Use a comma to separate vectors as needed.) H is not a subspace of [R2 because the scalar 4 and the vector |:| show that H |::l closed under Z Let H = Span{v1 ,v2} and K = Span{v3,v4}, where v1, v2, v3, and v4 are given below. 4 2 5 o v1= 1 .v2= 5 ,v3= 1.v4= 14 5 3 1 6 Then H and K are subspaces of R3. In fact, H and K are planes in R3 through the origin, and they intersect in a line through 0. Find a nonzero vector w that generates that line. <:> w=D [Hint: w can be written as c1v1 + c2v2 and also as c3v3 + c4v4. To build w, solve the equation c1v1 + c2v2 = c3v3 + c4v4 for the unknown cj's.] Determine Whether the set HI 3 linearly independent and whether the set spans R3. . . . Which of the following describe the set? Select all that apply. A. The set spans R 3. B. The set is a basis for R3. C. The set is linearly independent. D. None of the above are true