Consider the linear system: -x + 3x3 + x4 = 4 2x1 - 2x2 - 3x4...

 

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Consider the linear system: -x + 3x3 + x4 = 4 2x1 - 2x2 - 3x4 = -18 -3x1 + x2 x3 + 2x4 = 16 - -2x1 x2+2x3 - =-6 a. (1 pt) Rewrite the system of equations in Ax = b form. b. (6 pts) By hand, find rank(A) and rank(A|b) by using Gaussian elimination to reduce A and (Alb) to row echelon form (ref). c. (2 pts) Determine whether the system of equations is consistent or inconsistent. If the system is consistent, determine, without solving the linear system, whether it has a unique solution or infinitely many solutions. d. (3 pts) Solve the linear system (i.e. determine x1, x2, x3 and x4) by performing back- substitution. e. (3 pts) Verify your solution for parts (b) and (d) using the rank () and rref() in MATLAB. Activate Wi to Sottin Consider the linear system: -x + 3x3 + x4 = 4 2x1 - 2x2 - 3x4 = -18 -3x1 + x2 x3 + 2x4 = 16 - -2x1 x2+2x3 - =-6 a. (1 pt) Rewrite the system of equations in Ax = b form. b. (6 pts) By hand, find rank(A) and rank(A|b) by using Gaussian elimination to reduce A and (Alb) to row echelon form (ref). c. (2 pts) Determine whether the system of equations is consistent or inconsistent. If the system is consistent, determine, without solving the linear system, whether it has a unique solution or infinitely many solutions. d. (3 pts) Solve the linear system (i.e. determine x1, x2, x3 and x4) by performing back- substitution. e. (3 pts) Verify your solution for parts (b) and (d) using the rank () and rref() in MATLAB. Activate Wi to Sottin