Solve system of equations, Algebra

Solve out the following system of equations by using augmented matrices.

3x - 3 y - 6 z = -3

2x - 2 y - 4 z = 10

-2x + 3 y + z = 7


Following is the augmented matrix for this system.

1029_Solve system of equations.png

We can obtain a 1 into the upper left corner by dividing by the first row by a 3.

1138_Solve system of equations1.png

Next we'll obtain the two numbers under this one to be zeroes.

2210_Solve system of equations2.jpg

And we can end. The middle row is all zeroes apart from the final entry that isn't zero. Note that it doesn't matter what the number is as long as it isn't zero.

Once we reach this kind of row we know that the system won't contain any solutions and therefore there isn't any cause to go any farther.

Okay, let's see how we solve out a system of three equations along with an infinity number of solutions along with the augmented matrix method.  This instance will also illustrate an interesting idea regarding systems.

Posted Date: 4/8/2013 6:00:28 AM | Location : United States

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