Show that the set of all pairs of real numbers (x, y) with the operations (X1, Y1) + (x2, Y2) = (x1 + x2 + 1, y1 + Y2+ 1) and k (*1, Y1) = (kx1, kyı) is not a vector space.

Suppose v is a nonzero position vector in xyz-space. How many position vectors with length 2 in xyz-space are orthogonal to v?

01 3.) Verify the Cauchy - Sahorz inequality and the triangle inequality for the vectors. 3. x=(2, 0₁-1) (4,0,-2) ¡y = 4.) x=(7,0,2, 6), y =(3, 8, 4, 1) 5.) 6.) x - (1₁-1, 1,-1, 1), y=(3, 0, 0, 0, 2) = (1,0,0,1), y=(-1,0,0,1).,

2. If a set of vectors contains at least 2 vectors that are scalar multiples of each other, then the set is linearly dependent.