Question

053/1 polnls Previous Answo TanFin12 2.3.011 Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linesSequations, do representing the columns in turn.) 10 0 0 2] 0 1 0 0-s 0 0 1 17 0 000 o (a) Determine whether the system has a solution. O The system has one solution. o The system has infinitely many solutions. O The system has no solution. (b) Find the solution or solutions to the system, if they exist. (If there is no solution, enter NO SOLUTION. If there are infinit and/or s.) (x1, x2, x3, x4)-(1 Show My Work (optlonat Submit Answer Save Progress 6、 +--11 points TanFin12 2.301 5.CMl. Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If th

Answer 1

Let us consider the Augmented matrix in row-reduced form is [A/b] = [1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 2 -5 7 0] rightarrow 1 here, number of non-zero rows = 3 number of unknowns n = 4 therefore Rank of A = 3 Rank of [A/b] = 3 therefore Rank of A = Rank of [A/b] = 3 < (4 = n) a) hence, the system has infinitely many solutions. B) By backward substitution in 1, we get x_1 = 2 x_2 = -5 x_3 + x_4 = 7 let x_4 = t then x_3 = 7 - t therefore(x_1, x_2, x_3, x_4) = (2, -5, 7 - t, t)