Use augmented matrices to solve the system, Algebra

Utilizes augmented matrices to solve out each of the following systems.

x - y = 6

-2x + 2 y = 1

Solution

Now, already we've worked this one out therefore we know that there is no solution to this system. Let's see what the augmented matrix method provides us when we try to use it.

We'll begin with the augmented matrix.

1682_Use augmented matrices to solve the system.png

Notice that already we've got a 1 in the upper left corner therefore we don't have to do anything with that.  Thus, we next have to make the -2 into a 0.

616_Use augmented matrices to solve the system1.png

Now, the next step has to be to get a 1 in the lower right corner, however there is no way to do that without varying the zero in the lower left corner. That's a problem, since we must have a zero in that spot plus a one in the lower right corner. What it tells us is that it isn't possible to put this augmented matrix form.

Now, go back to equations & see what we've got in this case.

x - y = 6

0 = 13 ???

The first row only converts back into the first equation. However, the second row converts back to nonsense. We know it isn't true so that means that there is no solution.  Keep in mind, if we attain a point where we contain an equation that just doesn't make sense we have no solution.

Note that if we'd gotten

We would have been okay as the last row would return the equation y = 0 so don't get confused among this case and what we in fact got for this system.

314_Use augmented matrices to solve the system2.png

                   Let's sum up what we learned in the previous set of examples. First, if we contain a row wherein all the entries except for very last one are zeroes & the last entry is NOT zero then we can stop & the system will have no solution.

Next, if we obtain a row of all zeroes then we will have infinitely several solutions.  We will then have to do a little more work to get the solution & the number of equations will determine how much work we have to do.

Now, let's see how some systems along with three equations work.  The no solution case will be alike; however, the infinite solution case will have a bit worked to do.

Posted Date: 4/8/2013 5:58:03 AM | Location : United States







Related Discussions:- Use augmented matrices to solve the system, Assignment Help, Ask Question on Use augmented matrices to solve the system, Get Answer, Expert's Help, Use augmented matrices to solve the system Discussions

Write discussion on Use augmented matrices to solve the system
Your posts are moderated
Related Questions

Example    If 8 ×10 14  joules of energy is released at the time of an earthquake what was the magnitude of the earthquake? Solution There actually isn't much to do here o

A police academy is training 14 new recruits. Some are working dogs and others are police officers. There are 38 legs in all. How many of each type of recruits are there?


determine slope of 2y = -x + 10

Would like to have materials in Algebra 1 . something that will pertain to our 2015-2016 teks

Lisa and Judy read mystery novels. Judy has read three fewer than five times as many as Lisa. Equation: J=5L-3 Lisa: Judy:



I''m having trouble with this problem..t squared-16 divided by t squared minus-t-20