Gauss Elimination Method Solved Problems

Gauss Elimination Method Solved Problems-16
It's to the right of this one, which is what I want for reduced row echelon form. And to zero this guy out, what I can do is I can replace the first row with the first row minus the second row. 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.

It's to the right of this one, which is what I want for reduced row echelon form. And to zero this guy out, what I can do is I can replace the first row with the first row minus the second row. 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.

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

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

My second row is 0, 1, 2, and then I have a minus 3, the augmented part of it.

I'm replacing the first row with the first row minus the second row.

Each pivot entry in each successive row is to the right of the pivot entry before it.

My pivot entries are the only entries in their columns. So let's go back from the augmented matrix world and kind of put back our variables there.

The process of row reduction makes use of elementary row operations, and can be divided into two parts.

The first part (sometimes called forward elimination) reduces a given system to row echelon form, from which one can tell whether there are no solutions, a unique solution, or infinitely many solutions.

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.

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