V = {ax² + bx + 3|a, b ≤ R} ≤ P2.

Q3: Determine which of the following vectors are in span -2 If the vectors are in the span write them as a a linear combination of the above vectors, otherwise give a brief reason why the vector isn't in the span. (a) [1 2 8 1] (b) [2 4 -5 8] (c) [-3 7 11 11]

-0---0 = 1. Which of these vectors is in the span of ₁, 2, 3? Justify your answers. For this entire problem set, consider the vectors #₁ = (a) -B (b) B -B (c) 2. (a) Describe the span of ₁, 2, 3 as a set of points in R³. (b) Is the span all of R³? 3. (a) Show that ws is in the span of ₁, ₂. and 3 = (b) Suppose 6 = 2w1 + ₂-33. Without calculating 6, show that b is in the span of w₁, 02. (c) Now calculate b using the given linear combination and using the linear combination you found. You should get the same vector.

Let u1, U2, ..., un be a set of vectors, and suppose there are nontrivial solutions to x11x2u2+ +xnun = 0 Explain why, if x is a free variable, you can always express u; in terms of the vectors corresponding to the basic variables.

b. Please provide a well explained answer for the follwoing. And explain how to add/subtract vectors? What is the geometric meaning? And what is R^n? what is an ordered n-tuple?

1.) If you have 10 vectors in RIO which do they span Ro? Explain your answer are linearly independent,