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

2x+y/x+3y=-1/7and 7x+36y=47/3 hence find p if xy=p=x/y

Activity 1: Graphing To fill an order for Sizzlin'' Sauce sauces, you bought 1050 green peppers and 1200 hot chili peppers. • Write and graph a system of inequalities to represent

Solve following equations.                                         y -6 - 9 y -3 + 8 = 0 Solution y -6 - 9 y -3 + 8 = 0 For this part notice that, -6 = 2 (

To find the calorie density (D) in calories per ounce of food that contains c carories and weight w ounces is given by D=C/w

Example   Find out all the zeroes of P ( x ) = x 4 - 7 x 3 + 17 x 2 -17 x + 6 . Solution We found the list of all possible rational zeroes in the earlier example.  Follo


Simpler method Let's begin by looking at the simpler method. This method will employ the following fact about exponential functions. If   b x   = b y      then          x


how do i find the are of a triangular prism if the number that i multiply is an odd number and i have to divide by 2