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

Percentage profit and loss, #a grocer buys a box of 200oranges for $25 he s...

#a grocer buys a box of 200oranges for $25 he sells them for 15c caluclate his percentage profit

Product rule (f g)' = f ' g + f g', Product Rule: (f g)′ = f ′ g + f g′ ...

Product Rule: (f g)′ = f ′ g + f g′ As with above the Power Rule, so the Product Rule can be proved either through using the definition of the derivative or this can be proved

The parallelogram, love is a parallelogram where prove that is a rectangle...

love is a parallelogram where prove that is a rectangle

#titl., class 10 Q.trigonometric formula of 1 term

class 10 Q.trigonometric formula of 1 term

LPP, howto know whether a region is bounded or not

howto know whether a region is bounded or not

Derivatives of exponential and logarithm functions, Derivatives of Exponent...

Derivatives of Exponential and Logarithm Functions : The next set of functions which we desire to take a look at are exponential & logarithm functions. The most common exponentia

Examples of play and learning maths, Here are a few examples of some team g...

Here are a few examples of some team games. The teams can be small (1-3 children) or big (15-20 children). We start with some games for small children. a) One team places a numb

Value delivery, What do you mean by value delivery

What do you mean by value delivery

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