Solve the system by finding the reduced row-echelon form of the augmented matrix.

x-4y-2z=2

2x-11y-10z=13

-x+6y+6z=-8

reduced row-echelon form:

1 -4 -2 2

0 1 -10 -3

0 0 0 0

(It's wrong, and I don't know why ? )

If there is one solution, give its coordinates in the answer spaces below.

If there are infinitely many solutions, enter z in the answer blank for , enter a formula for in terms of in the answer blank for and enter a formula for in terms of in the answer blank for .

If there are no solutions, leave the answer blanks for , and empty.

How can I find my X, Y ,Z ? Is it going to be Zero ?!

The reduced row-echelon form is

The solutions to the system of equations are:

Step-by-step explanation:

To solve this system of linear equations,

you must:

Step 1: Transform the augmented matrix to the reduced row echelon form.

In an augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.

This is the augmented matrix that represents the system.

It can be transformed by a sequence of elementary row operations to the matrix.

There are three kinds of elementary matrix operations.

Using elementary matrix operations, we get that

Row Operation 1: add -2 times the 1st row to the 2nd row

Row Operation 2: add 1 times the 1st row to the 3rd row

Row Operation 3: multiply the 2nd row by -1/3

Row Operation 4: add -2 times the 2nd row to the 3rd row

Row Operation 5: add 4 times the 2nd row to the 1st row

Step 2: Interpret the reduced row echelon form

The reduced row echelon form of the augmented matrix is

which corresponds to the system

The system has infinitely many solutions.

step-by-step explanation:

for volume, add base x height x width

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