Use gauss-jordan row reduction to solve the given system of equations. hint [see examples 1-6.] (if there is no solution, enter no solution. if the system is dependent, express your answer in terms of x, where y = y(x), z = z(x), and w = w( x + y + 5z = −2 y + 6z + w = 3 x + 3y + 11z + 2w = 1 x + y + 5z + w = −2

The augmented matrix for the system can be written as ...

where the order of the variables is x, y, z, w. After subtracting the first row from the 3rd and 4th rows, this becomes ...

Then subtracting twice the second row from the third, you have ...


The 4th row tells you w = 0.
The third row tells you z = -3/-6 = 1/2.
Substituting these values into the equation for y gives y +6/2 +0 = 3, so y = 0.
Finally, substituting into the equation for x, we get x +0 +5/2 = -2, so x = -9/2.

The solution is (x, y, z, w) = (-9/2, 0, 1/2, 0).

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