gauss elimination with parameters

Posted on 2008-11-19
Last Modified: 2016-02-10
I'm breaking my head trying to figure out what i'm doing wrong,
i'm support to eliminate the following equations using Gauss elimination system

and i'm suppose to figure out for which a,b (which are Parameters) the system has One solution/Infinit Solutions/No solutions - if there's infint solutions i'm suppose to write the general solution for the system.
now it's all pretty basic in the begining

1    b  1  3
1  2b  1  4 R2->R2-R1
a    1  1  4 R3->R3-aR1

which leads me to

1   b           1  3
0   b           0  1       * i can reach the first value using /:b , i then get y=1/b
0  1-ab   1-a  4-3a

from here i'm puzzled as there's no way to carry on the elimination (if i'm doing it right)
Question by:d3bugg3r
    LVL 26

    Expert Comment

    You are making things too complicated.

    What happens if   a = b = 1 ??

    What values will make the 1st and 3rd equations wierd??
    LVL 3

    Author Comment

    I dont see how it's possible, it will give the following result for the 3rs equation:
    0 0 0 0 1 which is not possible, not as a solution anyway.
    LVL 26

    Expert Comment

    What happens to the 1st and 2nd equations if   a = b = 1 ??
    You don't have to solve them, just look at them.

    LVL 3

    Author Comment

    yes, it works out... but it doesnt for the 3rd so i cannot use those values as answer.
    and i have to define if for those two parameters there's uniqe solution, unlimited solutions or no solutions (like if b=0 then 1/0 on the second equation isnt possible)
    LVL 26

    Accepted Solution

    There are three cases to consider:

    1st and 2nd    ==>   a = b = 1    ==>  No solutions

    1st and 3rd    ==>   a=1  b=0.5  ==>  Infinite solutions

    2nd and 3rd   ==>  b=0 (which you found)  ==>  No solutions

    I'm pretty sure that all other cases have single solutions.
    LVL 22

    Assisted Solution

    Whenever you have an equation involving a product like
    r * s = t

    When t is zero, at least one of r and s must be zero
    When t is nonzero, both r and s must be nonzero

    Also, whenever you want to eliminate a factor like in
    a*b = 1
    to get
    a = 1/b
    You simply cannot do that unless you have proven that b is nonzero.


    Write Comment

    Please enter a first name

    Please enter a last name

    We will never share this with anyone.

    Featured Post

    What Is Threat Intelligence?

    Threat intelligence is often discussed, but rarely understood. Starting with a precise definition, along with clear business goals, is essential.

    Suggested Solutions

    Have you ever thought of installing a power system that generates solar electricity to power your house? Some may say yes, while others may tell me no. But have you noticed that people around you are now considering installing such systems in their …
    Lithium-ion batteries area cornerstone of today's portable electronic devices, and even though they are relied upon heavily, their chemistry and origin are not of common knowledge. This article is about a device on which every smartphone, laptop, an…
    Need more eyes on your posted question? Go ahead and follow the quick steps in this video to learn how to Request Attention to your question. *Log into your Experts Exchange account *Find the question you want to Request Attention for *Go to the e…
    Excel styles will make formatting consistent and let you apply and change formatting faster. In this tutorial, you'll learn how to use Excel's built-in styles, how to modify styles, and how to create your own. You'll also learn how to use your custo…

    761 members asked questions and received personalized solutions in the past 7 days.

    Join the community of 500,000 technology professionals and ask your questions.

    Join & Ask a Question

    Need Help in Real-Time?

    Connect with top rated Experts

    9 Experts available now in Live!

    Get 1:1 Help Now