SOLUTION: Use matrices to solve the system. (If the system has infinitely many solutions, express your answer in terms of c, where x = x(c), y = y(c), and z = c. If the system has no solutio

Question 661768: Use matrices to solve the system. (If the system has infinitely many solutions, express your answer in terms of c, where x = x(c), y = y(c), and z = c. If the system has no solution, enter NONE for each answer.)
x-2y-3z=-5
2x+y+z=9
x+3y-2z=2
(x,y,z)=?
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!


Hi, there--

Set up your 3x4 augmented matrix using the coefficients and constants from the three 
equations.

 1, -2, -3, -5
 2, 1, 1, 9
 1, 3, -2, 2

(NOTE: The interface with algebra.com is not that good at drawing matrices. I typed the rows 
in comma-separated formate.)

You want to perform a series of row operations to translate this matrix to reduced row echelon 
form (rref) if possible.

Add -2*Row1 to Row2:
1, -2, -3, -5
0, 5, 7, 19
1, 2, -2, 2

Add -1*Row1 to Row3:

1, -2, -3, -5
0, 5, 7, 19
0, 5, 1, 7

Multiply (1/5)*Row2.

1, -2, -3, -5
0, 1, 7/5, 19/5
0, 5, 1, 7

Add 2*Row2 to Row 1

1, 0, -1/5, 13/5
0, 1, 7/5, 19/5
0, 5, 1, 7

Add -5*Row2 to Row3.

1, 0, -1/5, 13/5
0, 1, 7/5, 19/5
0, 0, -6, -12

Multiply (-1/6)*Row3.

1, 0, -1/5, 13/5
0, 1, 7/4, 19/5
0, 0, 1, 2

Add 1/5*Row3 to Row1.

1, 0, 0, 3
0, 1, 7/5, 19/5
0, 0, 1, 2

Add -7/5*Row3 to Row2.

1, 0, 0, 3
0, 1, 0, 1
0, 0, 1, 2

The matrix is now in rref. (x, y, z = 3, 1, 2)

~Mrs. Figgy

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