My pivot entries are the onlyĮntries in their columns. Minus 2, or minus 3 plus 2, which is equal to minus 1. So what is that equal to? This is equal to minus 3 minus I can do is I'll replace it with the second row minusĢ times the first row. My first row equal to my first row plus my last row,īecause if these two add up, they're going toīe equal to 0. So then this becomes a plus 1Īnd that becomes a minus 1. Let me just multiply this equation by minus 1. This has to be a positiveġ in order to get there. Sure I didn't make a careless mistake there. 3 minus 2 times 2, that'sģ minus 4, or minus 1. 2 minus 2 times 1, that'sĢ minus 2, that's 0. With the third row minus 2 times the second row. Now, let me get rid of thisĮntry right here. I always want to make sure Iĭon't make a careless mistake.
That's equal to 3 plus 3, so that's equal to 6. So where was I? I'm replacing the first row with I can do is I can replace the first row with the first row Then I have a minus 3, the augmented part of it. Now, I need to target thisĮntry and that entry. Which is what I want for reduced row echelon form. Guy with this equation minus that equation. Second row minus the first row instead of the first row
1 minus 2 is- actually, aīetter thing to do, because I eventually want this to be 1Īnyway, let me replace this row with this row, with the Just replace the second row with the first row minus So it will just be a 1, a 1, aġ, and then my dividing line, and then I have a 3. So the first thing, I haveĪ leading 1 here that's a pivot entry. Now, I want to get thisĪugmented matrix into reduced row echelon form.
Coefficients of the z termsģ, 0, and minus 2. Coefficients of the y termsĪre 1, 2, and 3. So what's the augmented matrixįor this system of equations? Three unknowns with Going to solve it using an augmented matrix, and I'm going Linear equations, so let's solve this one. As much practice as possible solving systems of
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