In matrix form, the system of equations S = {x + 2y + 2z - 2w = 1 x + 3y + z - 4

Question

In matrix form, the system of equations S = {x + 2y + 2z - 2w = 1 x + 3y + z - 4w = -1 6x + 14y + 14z - 12w = -2 11x + 27y + 25z - 26w = -8 yields the augmented coefficient matrix (x 1 1 6 11 y 2 3 14 27 z 2 1 14 25 w -2 -4 -12 -26 rhs 1 -1 -2 -8) for which a row echelon form (REF) is (x 1 0 0 0 y 2 1 0 0 z 2 -1 -2 0 w -2 -2 -2 -2 rhs 1 -2 2 -1). Continue the reduction of the augmented matrix to produce its reduced row echelon form (RREF) Fill in the blanks below to give the complete solution to the system. The entry for a free variable should be itself. x = y = z = w =

Explanation / Answer

Your matrix

Find the pivot in the 1st column in the 1st row

Eliminate the 1st column

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

Eliminate the 2nd column

Make the pivot in the 3rd column by dividing the 3rd row by 4

Eliminate the 3rd column

Make the pivot in the 4th column by dividing the 4th row by -2

Eliminate the 4th column

Solution set:

x = 10

y = -5/2

z = -3/2

w= 1/2

X1 X2 X3 X4 b 1 1 2 2 -2 1 2 1 3 1 -4 -1 3 6 14 14 -12 -2 4 11 27 25 -26 -8

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