The following set S of vectors spans R4. Find a subset BCS that is a basis for R4. S = 8 -3 Number of vectors: 1 {:} B =

Are the following vectors a basis of R²?

Suppose that v = (v1, v2, ..., vn) and û = (u₁, U2, ..., Un) are a pair of n-dimensional vectors. Assume that each component of the vector is a real number, so 7 and u are both members of the set R¹. We will say that and u 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, u) which asserts that n dimensional vector is almost the same as ū. Tip: It is not legal to say i v to refer to a component of v, because is not a set. Instead, use vi to refer to the ith component of v. What set would i belong to in this case?

(1, 1,0,0,0) be two binary vectors. Compute the Hamming 3. Let y = (1,0,0,0, 1) and z = distance and the Jaccard distance between y and z manually. (Do not use R.)