Question

linear algebra

do both drawing in part A and B

2. Consider the set and let addition and scalar multiplication be the standard operations on vectors in R2 (a) State a specific numerical example that shows that V is not closed under vector addition, then draw a sketch for your example, shading the region V, and drawing your example vectors and their linear combination with the parallelogram method that shows V is not closed under vector addition (b) Provide a detailed proof that V is closed under scalar multiplication, regardless of whether the scalar is a negative or nonnegative real number. Draw a second sketch of the region V and draw a vector along with the positive and negative scalar multiples of your vector, showing that the resulting vectors remain in the region V.

Answer 1

Consider the set v = {[x y] = xy greaterthanequalto 0, x, y elementof R} and let addition and scalar multiplication be the standard operators on vectors in R^2 (a) Let a = (1 2) elementof V as 1 -2 > 0 b = (-2 -1) elementof V as (-2) (-1) = z > 0 But a + b = (1 2) + (-2 -1) = (-1 1) notelementof V as (-1) (1) = -1, 0