Use Gauss-Jordan row reduction to solve the given system of equations. (If there

Question

Use Gauss-Jordan row reduction to solve the given system of equations. (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x) and z = z(x).) x + y + 6z = 3 1/3x + 1/3y + 2/3z = 1 1/2x + z = 0 (x, y, z) = () Use Gauss-Jordan row reduction to solve the given system of equations. (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x) and z = z(x).) -1/2x + y - 1/2z = 0 -1/2x - 1/2y + z = 0 x - 1/2y - 1/2z = 0 (x, y, z) = ()

Explanation / Answer

1)

Your matrix

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

Eliminate the 1st column

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

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

x = -3

y = -3

z = 3/2

X1 X2 X3 b 1 1 1 6 3 2 1/3 -1/3 2/3 1 3 1/2 0 1 0

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