Suppose that v = (v1, v2, ..., vn) and ū = (u₁, U2, ..., Un) are a pair of n-dimensional vectors. Assume that each component of the vector is a real number, so v and u are both members of the Set R¹ We will say that 7 and ū are "almost the same" when every component of is close to every component of ū. That is, v₁ is close to u₁, v2 is close to u2, etc (practically speaking, "close" means that their absolute difference is small). Assume that we are given the predefined predicate CloseTo(x, y) and the integer constant n. Use them to write a formal definition of the new predicate Almost The Same (7, ū) which asserts that ʼn dimensional vector is almost the same as ū.

5.) Sketch the given vectors Vand W. On your sketch, draw in v v+w, and v-w. OV=(2, 1) and W=(1, 2) by v= (0₁4) and w = (2₁-1) v=(2,3₁-6) ond w=(-1,1,1)

Let v= (4,5,8) and w=(-10,-8,9) be vectors. Find the scalar component of v in the direction of w. Also, write v as a sum of two vectors, one of which is parallel to w and the other of which is perpendicular to w.

Let v1 = <0, 1>, v2 = <-1, 0>, w = <-7, 1> vectors ∈ R2. Does the set {v1, v2} span R2?