Question

MPORTANT: If you are going to write please make sure your writing is neat, legible, and easy to read. Please write in print (not cursive). Thank you

IMPORTANT: I know the answer is given bellow, but I do have a couple of conceptual things I'd like explained. I know it may be a bit silly, but please explain to me what it means for a matrix to be "linearly independent" and why the matrix (in this case) is not linearly independent?-(This question is because of the first possibility given). Also, could you please explain what R³ is/means? Why isn't that necessarily true in this particular case?

54. Given that a system of equations has augmented matrix (A[b] that row reduces [1 -2 1 -1 0 to the row echelon form 0 0 2 3-2. Which of the following must be true 0 0 0 0 0 about the system. Mark all that apply. The columns of A are linearly independent. The columns of A span all of R3 The rank of A is 2. The system has 3 free variable. The system is inconsistent. The system has a unique solution. The system has infinitely many solutions.

Answer 1

73 IR means the set of rechas of the perm (1,4,7), wheue. X, Y, ZER. rechues o cl, 12. lo aue lineanlyindependentif - Cor Glot Encone o of a n = o. Hew the columns Quot lineadly independent since, 2/6+/-2) - (0) ( 10 Columne donor Spar. R3 &mu the vecher / 8') s cannot be wother as a lincan combbabon of the CW Aren rechas Since the number of piroks are a in the pref au hanc QanKA = 2 me Lytem bas i nitely mary Holub ons since the number of equations is len than the number of Vauiable and the equbone aue consistent. Thue the system abe donot have an unique solubon