# SOLUTION: how to solve augmented matrices

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 Question 224853: how to solve augmented matrices Answer by LtAurora(115)   (Show Source): You can put this solution on YOUR website!There is no one way to solve an augmented matrix. You have to use row operations to try and get one of the rows with a coefficient of 1. For example a 3x3 augmented matrix: [1 -2 3 | 9] [0 1 3 | 5] [0 0 1 | 2] The last row tells us that z=2. So we can go back and substitute that into our second equation which is: . This would give us what y is. Then we could substitute both y and z into the first equation to get what x is equal to. The row operations you are allowed to do are: 1. Interchange two rows. (So, just move row 1 down and row 2 up) 2. Multiply a row by a non-zero constant (So, fractions and any whole numbers) 3. Add a row to another (So, row 1 + row 2 can be the new row 2. You can also multiply row 1 by something while adding it to row 2, like row 1 + row 2 is the new row 2.) Unfortunately, all of these operations are done by trial and error to try to get the augmented matrix to look something like the example, where you get z=some number. The example problem I referenced had row 3 start out as: [2 -5 5 | 17], and about 5 steps later looked like the example. So, you've got a bit of work to solve these things. Hope this helps a bit, otherwise post the problem you're having trouble with.