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

Pharmacy, prescription has a 35% mark up with a 5.66 dispense fee one table...

prescription has a 35% mark up with a 5.66 dispense fee one tablet is 15.70 and how much would 3 tablets cost?

Deacay, Ask quesThe above model describes the exponential decay of chemical...

Ask quesThe above model describes the exponential decay of chemical element. t is the time in years, Q(0) is the initial amount of the chemical element, Q(t) is the amount of chemi

Student, the weight of a body above the surface of earth varies inversely w...

the weight of a body above the surface of earth varies inversely with the square of the distance from the center of the earth. if maria weighs 125 pounds when she is on the surface

Proportions, A kilometer is about 5/8 mile.About how many miles are in 4 2/...

A kilometer is about 5/8 mile.About how many miles are in 4 2/5 kilometers? How would I set a proportion?

Problem, Solve the system algebraically. x - 2y - 3z = negative-1 2x + y ...

Solve the system algebraically. x - 2y - 3z = negative-1 2x + y + z = 6 x + 3y - 2z = negative13

Exploring conic sections, graph and identify the conic section and describe...

graph and identify the conic section and describe the graph and its lines of symmetry then find the domain and range 3y^2 - x^2 = 25

#rigid non rigid transformations, #can u tell me some things on rigid and n...

#can u tell me some things on rigid and non rigid transformations

Uniform motion, How do you do uniform motion? i am stuck on some problems

How do you do uniform motion? i am stuck on some problems

Math question, The Timbuktu post office has only 3 cents and 7 cents stamps...

The Timbuktu post office has only 3 cents and 7 cents stamps having run out of all other denominations. What are the six amounts of postage that cannot be created? How do you know

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