(a) Does the subset of all vectors with a₂ = 0 constitute a vector space? If so, what is its dimension; if not, why not? (b) What about the subset of all vectors whose z component is 1? (c) How about the subset of vectors whose components are all equal?

-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.

The following question is from linear algebra first year: Factors the vector (6, -5, -1)t into three components a,b,c that satisfy the following conditions: a depends on (2,0,1)t, b depends on (1,2, 0)t and c is orthogonal to a and b. Please show it step by step. Can we get integers as answers?

5.PS-16 Question Help A shoe store uses a 60% markup for all of the shoes it sells. What would be the selling price of a pair of shoes that has a wholesale cost of $55? The selling price would be $ (Round to the nearest cent as needed.) Enter your answer in the answer box and then click Check Answer. All narte chowing Review progress Question 9. of 9 pe here to search

Show that a set of vectors, which contains a set of linearly dependent vectors, is linearly dependent. What is the analogous statement about linearly independent vectors?