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

Find the 20th term of arithmetic progressions, Find the 20 th term from th...

Find the 20 th term from the end of the AP 3, 8, 13........253. Ans:    3, 8, 13 .............. 253 Last term = 253 a20 from end = l - (n-1)d 253 - ( 20-1) 5 253

Explain polynomials, P OLYNOMIALS : It is  not  once  nor  twice  b...

P OLYNOMIALS : It is  not  once  nor  twice  but  times  without  number  that the  same ideas make  their  appearance in the  world. 1.  Find the value for K for which

Math, i need help in math

i need help in math

Complex, find all the 8th roots of (19+7i)

find all the 8th roots of (19+7i)

Envision math common core, how do i write a conjecture about the sum of two...

how do i write a conjecture about the sum of two negative integers.

Solve the initial value by laplace transform method, Question: Solve the i...

Question: Solve the initial value problem 2x'' +x'-x =27 Cos2t +6 Sin 2t, x(0)=2 , x'(0)= -2 by using Laplace transform method.

Extrema- minimum and maximum values, Extrema : Note as well that while we ...

Extrema : Note as well that while we say an "open interval around x = c " we mean that we can discover some interval ( a, b ) , not involving the endpoints, such that a Also,

Assemble the coefficient matrix and solve the linear system, Solve discrete...

Solve discrete harmonic mapping of a given surface patch (suppose the surface is genus-0 and with one boundary) 1. Map the boundary loop onto a unit rectangle using chord-length

Define multiplication rule in probability, Q. Define Multiplication Rule in...

Q. Define Multiplication Rule in probability? Ans. A family has two girls, Ann and Barb, and three boys, Carl, David and Earl, in it. In how many ways can the mother pick

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