use the given example to answer!!!!!

Determine whether the system Ax : b has a unique solution given a matrix A and a vector b. (a) b: [1.142 [ 2 1] 2 ,4 72 (b) 14 2 4 b: 10 ,A= 2 2 5 1 1 1) 1 1 1 5 Correct Given A = 2 0 1 | and b = 0 , does Ax = b have 1 0 0 1 -1 1] 12 a unique solution? The reduced echelon form of A is A' = 0 1 0 0 1 O Yes Since the columns of A' are independent, the only O No solution to A'x = 0 is the zero vector. Thus, null(A) = 0. By the theorem above, Ax = b has a unique solution. 2) 3 2 -1 4 2 Correct Given A = 1 0 2 3 and b = -4 , does The reduced echelon form of A is -2 -2 3 1 5 0 2 0 Ax = b have a unique solution? A= 0 O O Yes O No Since not all columns of A' are pivot columns, the corresponding system A'x = 0 has infinitely many solutions. Thus, null(A) / {}. By the theorem above, Ax = b does not have a unique solution