Sangeetha Pulapaka

STEP 1: Recall what are augmented matrices

and recall what are the elementary row operations

STEP 2: Write down the augmented matrix

To convert it into the final form we will start in the upper left corner and work in a counter-clockwise direction until the first two columns appear as they should be.

So, the first step is to make the red three in the augmented matrix above into a 1. We can use any of the row operations that we’d like to. We should always try to minimise the work as much as possible however.So, since there is a one in the first column already it just isn’t in the correct row let’s use the first row operation and interchange the two rows

STEP 3: Interchanging the two rows we get

STEP 4: Change the red three into a zero. This will almost always require us to use third row operation. If we add -3 times row 1 onto row 2 we can convert that 3 into a 0. Here is that operation.

STEP 5: Next, we need to get a 1 into the lower right corner of the first two columns. This means changing the red -11 into a 1. This is usually accomplished with the second row operation. If we divide the second row by -11 we will get the 1 in that spot that we need.

STEP 6:The final step is to turn the red three into a zero. Again, this almost always requires the third row operation. Here is the operation for this final step.