Linear Algebra: Matrix Algebra and Determinants

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(9) Let 1 2 l 1 l 1 2 0 l -3 2 4 3 2 U 0 0 1 O 2 be the matrix of coefcients for a linear system. Let 5 2 17 -7 A: I}: Do the following. (a) Find rank(A}. You may use Mathematics to nd the REEF of A. You must record the result. (b) Find all solutions of An: = [l where a: = ENEH (c) Find all solutions to As: = b. You can use Mathematics to compute the REF of the augmented matrix. (10) State whether each of the following sets of data are possible for the matrix equation AX = B. If possible, describe the solution set; i.e.ll tell whether there exists a unique solution, no solution or innitely solutions. Here1 [AIB] denotes the augmented matrix. (a) A E ngg, rank(A) = 4 and rankAlBJ) = 4. (b) A E M5\