Augmented matrices, Algebra

Assignment Help:

In this section we have to take a look at the third method for solving out systems of equations.  For systems of two equations it is possibly a little more complex than the methods we looked at in the previous section.  However, for systems with more equations it is possibly easier than using the method we saw in the previous section.

Before we discussed the method first we need to get some definitions out of the way.

An augmented matrix for system of equations is matrix of numbers wherein each row represents the constants from one equation (both the coefficients & the constant on the other side of the equal sign) and each of the columns represents all the coefficients for a single variable.

Let's consider a look at an example.  Here is the system of equations which we looked at in the previous section.

x - 2 y + 3z = 7

2x + y + z = 4

-3x + 2 y - 2 z = -10

Following is the augmented matrix for this system.

2478_Augmented Matrices.png

The first row contain all the constants from the first equation  along with the coefficient of the x in the first column, the coefficient of the y into second column, the coefficient of z into the third column and the constant in the final column.  The second row is constants from the second equation along with the similar placement and similarly for the third row. The dashed line show where the equal sign was placed in the original system of equations and is not always involved. This is mostly based on the instructor and/or textbook being used.


Related Discussions:- Augmented matrices

Complex solutions of quadratic equations, These are the only possibilities ...

These are the only possibilities for solving quadratic equations in standard form.  However Note that if we begin with rational expression in the equation we might get different so

Scientific notation, The average U.S. citizen consumes about 2.5 × 102 L of...

The average U.S. citizen consumes about 2.5 × 102 L of water per day for various uses. In 2013, there were about 3.16 × 108 U.S. citizens. About how many kiloliters of water were c

Arithmatic progression, find the sum upto n terms of the following sequence...

find the sum upto n terms of the following sequence 3+33+333+... n terms

Coordinates for the point - graphing, Coordinates for the point  The li...

Coordinates for the point  The listed first number is the x-coordinate of the point and the second number listed is the y-coordinate of the point. The ordered pair for any spec

Example of function evaluations, Given  f ( x ) = x 2 - 2 x + 8 and  g( x ...

Given  f ( x ) = x 2 - 2 x + 8 and  g( x ) = √(x+ 6) evaluate f (3) and g(3) Solution Okay we've two function evaluations to do here and we've also obtained two functions

Math, i am in 6th grade..... and just test prep

i am in 6th grade..... and just test prep

Solve 3x3 systems, how do I solve these types of equations?

how do I solve these types of equations?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd