- 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 Po 1 (117.97 KiB) Viewed 59 times
3. The matrix A for a system and its rref R are given below: A=⎣⎡110−2−10−135332⎦⎤R=⎣⎡100001000010⎦⎤ (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 []]