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

Related to MCA, AskIf y=e^(a?sin?^(-1) x), prove that (1 – x2)yn+2 – (2n + ...

AskIf y=e^(a?sin?^(-1) x), prove that (1 – x2)yn+2 – (2n + 1)xyn+1 – (n2 + a2)yn = 0. Hence find the value of yn when x = 0. question #Minimum 100 words accepted#

Comperative statics, Discuss comparative statics,Market model and Nationa i...

Discuss comparative statics,Market model and Nationa income model

Pre Calculus, 5 2 ----- - ----- x-1 x+1 ------------------...

5 2 ----- - ----- x-1 x+1 -------------------- x 1 ----- + ----- x-1 x+1

Vectors, A 10 m ladder of 150N is placed at an angle 30degrees to a smooth ...

A 10 m ladder of 150N is placed at an angle 30degrees to a smooth wall at point A and the other end (point B) on the ground. Assume that the weight of the ladder acts at its mid po

Method for simultaneous equations of two or more variables, Method In ...

Method In this method we eliminate either x or y, get the value of other variable and then substitute that value in either of the original equations to

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