Attempt to solve the following linear systems by using Gaussian elimination to f

Question

Attempt to solve the following linear systems by using Gaussian elimination to find a similar system whose coefficient matrix is in row echelon form.

If the system has a unique solution, give it (in point form.)

If the system is inconsistent, write NONE for the solutions.

If the system has is consistent and there are free variables, transform it to reduced row echelon form and find all solutions. (As before, write your general solutions in terms of the variables a, b, c, .... For example, (1,2-a+b,b,a).)

2x1 + z2 + 4x3 + 3x4 = 15 1 31 3x2 823 21t23

Explanation / Answer

(e)

Your matrix

Find the pivot in the 1st column and swap the 2nd and the 1st rows

Eliminate the 1st column

Find the pivot in the 2nd column in the 2nd row

Eliminate the 2nd column

Find the pivot in the 3rd column in the 3rd row (inversing the sign in the whole row)

Eliminate the 3rd column

Solution set:

x1 = 6 - 2t

x2 = 7 - 3t

x3 = -1 + t

x4 = t

t - free

(f)

Your matrix

Find the pivot in the 1st column and swap the 2nd and the 1st rows

Eliminate the 1st column

Make the pivot in the 2nd column by dividing the 2nd row by -3

Eliminate the 2nd column

Solution set:

x1 = 4/3 + (2/3)s - (5/3)t

x2 = 1/3 - (1/3)s + (1/3)t

t, s - free

X1 X2 X3 X4 b 1 2 1 4 3 15 2 1 0 1 1 5 3 0 1 1 2 6 4 3 3 8 7 31

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