Answer Happy

linear algebra
3. The matrix A for a system and its rref R are given below: A=⎣⎡​110−2​−10−13​5332​⎦⎤​R=⎣⎡​1000​0100​0010​⎦⎤​ (a) (5 points) Since R, and consequently A, have a pivot in every column, then A has full column rank. This means there are no free variables here, so that the nullspace is trivial. Which of the following is true for this system? A. Ax=b has 1 solution for every vector b. B. Ax=b has ∞ solutions for every vector b. C. Ax=b has either no solution or 1 solution for every vector b. D. Ax=b has either no solution or ∞ solutions for every vector b. (b) (7 points) Describe the column space, C(A) as the span of some set of vectors. Fill in what those vectors are below: Consider the following b vectors. Determine if there is a solution to the Ax=b for that vector. If there is, what is the x vector, if there isn't, prove it isn't by showing an augmented matrix R∣d] that clearly indicates there is no solution. (c) (4 points) b=⎣⎡​6612​⎦⎤​ C(A)=span b vectors. Determ vector, if there isn't, there is no solution. =b for that vector. If ugmented matrix R∣d]  If yes, then x=[] If no, then []] (d) (4 points) b=⎣⎡​5424​⎦⎤​ If yes, then x=[ If no, then []]