Trivial solution of equation, Mathematics

Assignment Help:

Specified a system of equations, (1), we will have one of the three probabilities for the number of solutions.

1.   No solution.

2.   Accurately one solution.

3.   Infinitely many solutions.

Before going on to the other section we require to see at one more situations. The system of equations in (1) is termed as a non-homogeneous system whether at least one of the bi's is not zero. If though all of the bi's are zero we identify the system as homogeneous and the system will be as,

a11 x1 + a12 x2 +................+a1n xn = 0

a21 x1 + a22 x2 +.............. +a2n xn  = 0

...................

an1 x1 + an2 x2 +............... +ann xn  = 0                                 ...................(2)

Now, notice that in the homogeneous case we are guaranteed to have the following solution.

x1 + x2+....... +xn  = 0

This solution is frequently termed as the trivial solution.

The fact given above can be modified to the following, for homogeneous systems.


Related Discussions:- Trivial solution of equation

Regression, Regression line drawn as y=c+1075x, when x was 2, and y was 239...

Regression line drawn as y=c+1075x, when x was 2, and y was 239, given that y intercept was 11. Caculate the residual

Parabola, please i need the answers to x^_7x+10 i want the vertex,axis of s...

please i need the answers to x^_7x+10 i want the vertex,axis of semetery,y intersect and the x intercept

Exponent, base also called what

base also called what

Law of cosines - vector, Theorem a → • b → = ||a → || ||b → || cos• ...

Theorem a → • b → = ||a → || ||b → || cos• Proof Let us give a modified version of the diagram above. The three vectors above make the triangle AOB and note tha

Time table, tips to memorize my time table

tips to memorize my time table

Math, Verify Louisville''s formula for y "-y" - y'' + y = 0 in (0, 1) quest...

Verify Louisville''s formula for y "-y" - y'' + y = 0 in (0, 1) question..

What are natural numbers and whole numbers, What are Natural Numbers and Wh...

What are Natural Numbers and Whole Numbers? Natural numbers are the numbers that you "naturally" use for counting: 1, 2, 3, 4, ... The set of whole numbers is the set of

Dr.., I need some material on Bachet equation

I need some material on Bachet equation

Numeric patterns, Kelli calls her grandmother every month Kelli also calls ...

Kelli calls her grandmother every month Kelli also calls her cousin.If Kelli calls her cousin in January, how many calls will Kelli have made to her grandmother and her cousin by t

Emi, calculation of emi %

calculation of emi %

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