For each of the systems of equations that follow,use Gaussian elimination to obtain an equivalentsystem whose coefficient matrix is in row echelonform. Indicate whether the system is consistent.If the system is consistent and involves no freevariables, use back substitution to find the uniquesolution. If the system is consistent and there arefree variables, transform it to reduced row echelonform and find all solutions. x1+ 2x2− 3x3+ x4= 1 −x1− x2+ 4x3− x4= 6 −2x1− 4x2+ 7x3− x4= 1

Question

For each of the systems of equations that follow,
use Gaussian elimination to obtain an equivalent
system whose coefficient matrix is in row echelon
form. Indicate whether the system is consistent.
If the system is consistent and involves no free
variables, use back substitution to find the unique
solution. If the system is consistent and there are
free variables, transform it to reduced row echelon
form and find all solutions. x1+ 2x2− 3x3+ x4= 1
−x1− x2+ 4x3− x4= 6
−2x1− 4x2+ 7x3− x4= 1

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