Gauss Elimination Method Solved Problems

Gauss Elimination Method Solved Problems-45
So what's the augmented matrix for this system of equations? So the first thing, I have a leading 1 here that's a pivot entry.

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And then 3 minus minus 3, so that's equal to 3 plus 3, so that's equal to 6.

I always want to make sure I don't make a careless mistake.

I figure it never hurts getting as much practice as possible solving systems of linear equations, so let's solve this one.

What I'm going to do is I'm going to solve it using an augmented matrix, and I'm going to put it in reduced row echelon form.

Now, I want to get this augmented matrix into reduced row echelon form.

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So let me replace this guy with this equation minus that equation.

So let me replace the third row with the third row minus 2 times the second row. 3 minus 2 times 2, that's 3 minus 4, or minus 1.

2 minus 2 times 1, that's 2 minus 2, that's 0.

For example, in the following sequence of row operations (where multiple elementary operations might be done at each step), the third and fourth matrices are the ones in row echelon form, and the final matrix is the unique reduced row echelon form.

Using row operations to convert a matrix into reduced row echelon form is sometimes called Gauss–Jordan elimination.


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