• please help me with questions problem 4 and problem 5 , which means all the questions included in the picture , I don't know why it keeps telling me I need to revise my question. there is no problems with my questions .
  

Safari ,XIN #8 56 X O A [In Q 2 97 158 BE F46:13 ... of 2 - ZOOM + Definition: We say that a subset S C R" is closed under vector addition if for all i, y E S we have a + y E S, and closed under scalar multiplication if for all T E S and c E R we have ci E S. Problem 4. Let A be an m x n matrix, let b E Rm, suppose that the linear system At = b is consistent, and let S be the solution set of AT = b. (a) Prove that S is closed under vector addition and scalar multiplication if and only if b = 0. (b) Let So be the solution set of the linear system AT = 0. Prove that for all v E S, we have S = {U+5 : TE So}. (c) Suppose A - -2 4 and 5 - Assuming S and So are as defined above, sketch S and So as subsets of R2 and briefly describe their geometric relationship to one another. Definition: Let n E N, and let A E Rnx be a square matrix whose (i, j)-entry is aij for each 1