Solve out the given system, Algebra

Solve out the following system of equations by using augmented matrices.

3x - 3 y - 6 z = -3

2x - 2 y - 4 z = -2

-2x + 3 y + z = 7

Solution

Notice that this system is approximately identical to the system in earlier example. The only difference is the number to the right of the equal sign in the second equation.  In this system it is two and in the previous example it was ten.  Altering that one number totally changes the type of solution that we're going to get.  Frequently this kind of simple change won't influence the type of solution that we get, however in some rare cases it can.

Since the first two steps of the procedure are identical to the previous part we won't discuss them. Here they are.

1603_Solve out the given system.png

 

We've got a row of all zeroes thus we instantly know that we've got infinitely several solutions. Unlike the two equation case we aren't going to stop however.  This looks like with a couple of row operations we can make the second column look as it is assumed to in the final form so let's do that.

1015_Solve out the given system1.png

In this case we were capable to make the second column look as it's assumed to and the third column will never look accurate.  Though, this is possible that the condition could be reversed and it would be the third column which we can make look correct and the second wouldn't look right. Every system is different.

Once we reach this point we go back to equations.

             x - 5z = 4

             y - 3z = 5

Now, both of these equations have a z and thus we'll move that to the other side in each equation.

                           x + 5z = 4

                           y + 3z = 5

It means that we get to pick the value of z for free & we'll write the solution as,

x = 5t + 4

y =3t + 5        

z = t

 where t refer to any real number

As there are an infinite number of ways to select t there are an infinite number of solutions to this system.

Posted Date: 4/8/2013 6:02:57 AM | Location : United States







Related Discussions:- Solve out the given system, Assignment Help, Ask Question on Solve out the given system, Get Answer, Expert's Help, Solve out the given system Discussions

Write discussion on Solve out the given system
Your posts are moderated
Related Questions
a farmer has a garden with 2 sides at right angles and the third side is 423ft.long.find the perimeter of the garden. if the angle between the shortest and the longest side is 58''

Multiply a Row by a Constant.   In this operation we multiply row i by a constant c and the notation will utilizes here is cR i .  Note that we can also divide a row by a constant


Find the number of permutations of them word helicopter

five years ago,you bought a house for $151,000, with a down payment of $30,000, which meant you took out a loan for $121,000. Your interest rate was 5.75% fixed. You would like t

Question 1: (a) Describe a binary operation on a set S. (b) Give the definition of a group. (c) State whether the following statements are TRUE or FALSE. Justify your

calculate this three-wire thread problem.1/2-20 with wire size 0.032"

there are some benches in a class room if 4 student sit on each benche 3bencha are left vacant and if 5 student sit each benche 3 student are left standing how many student are the

(x+a) (x+b) (x+c) =

what is the volume of a cube with side length 4 ?