For the following 123 parts say if the given space U, V, W is a subspace of Rn (n = 2, 3, 4 respectively in parts 123). If your answer is NO, justify it in some way - for instance say what about the space fails. If your answer is YES, you must show the 3 properties hold. They are not written on this page so you get a chance to first think and see if you remember them, and perhaps have to go look them up. You can find them in Theorem 4.2.1; conditions (a) and (b) are what Prof V called (1) and (2); additionally a subspace needs to be non-empty, which Prof V said you could replace with what she called the 0th condition. (If your TA told you how to check the 2 properties (a) (b) in one step, it is ok to just use that.) If still confused, read the book, re-read your lecture notes, and/or go to office hours. It is totally fine to show a TA your 1st draft of your HW solution for them to tell you if it's correct. In each case I have an "in other words" way of writing the subset; sometimes that re-casting can be helpful. Rn I write my subsets as {x € R" | blah} which is math notation for {x is an element of Rn such that it satisfies the given property}. (1) 1 8 7 1/2 In other words, U = {u € R² | Bu = b} (for matrix B as given above). (2) U = = {u € R² | 3 -2 u= W = { [:] 0 0 V = {v € R³||| i] x = [8]) 1 23 -3 37 V 1 0 In other words, V = {v € R³ | Av = 0} (for matrix A, vector b as given above). (3) a - 7c 2a + b a + 3b a + 2b + 6c | a, b, c = R} try to think for yourself why = {Cx} for appropriate 4 × 3 = In other words, WC R4 and W = span{w₁, W₂, W3} where... ( you should it is a span and a span of what vectors???) It is also possible to recast W matrix C and appropriate 3 × 1 column vector x.