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

Mixed numbers and improper fractions, how do you make the fraction 17 5ths ...

how do you make the fraction 17 5ths a mixed number?????

Function composition, Now we need to discuss the new method of combining fu...

Now we need to discuss the new method of combining functions. The new way of combining functions is called function composition. Following is the definition. Given two functions

Ratios, Lee is taking some friends on a picnic. They''ll need to follow a p...

Lee is taking some friends on a picnic. They''ll need to follow a path to get to the picnic spot. A map of the path is based on a scale of 1:30,000, in cm. If the path is 12 cm on

Algebra 2, Find the zeros of the function by using the quadratic formula. ...

Find the zeros of the function by using the quadratic formula. Simplify your answer as much as possible. g(x)= 2x^2+4x-12

Expanding brackets.., how to expand when asked to divide, multiply etc

how to expand when asked to divide, multiply etc

Find out angle of a triangle, Let a = 2 cm, b = 6 cm, and angle A = 6...

Let a = 2 cm, b = 6 cm, and angle A = 60°.  How many solutions are there for angle B   We must calculate b sin A .  If it is less than a , there will be

Turning points - polynomials, The "humps" where the graph varies direction ...

The "humps" where the graph varies direction from increasing to decreasing or decreasing to increasing is frequently called turning points .  If we know that the polynomial con

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