Undetermined system with no solutions?

  • Thread starter Thread starter Questions999
  • Start date Start date
  • Tags Tags
    System
AI Thread Summary
The discussion centers on demonstrating that the given system of equations has no solutions. It is noted that the system is undetermined due to having more unknowns than equations. The determinant of the matrix formed by the coefficients is initially stated to be non-zero, indicating linear independence, but later corrections reveal it is actually zero. The key point is that a linear combination of the equations leads to a contradiction, confirming the absence of solutions. Thus, the conclusion is that the system indeed has no solutions.
Questions999
Messages
151
Reaction score
0
So I have the system { 2x+3y+z-3v=2 ;x-y+2z+v=0 ;3x+2y+3z-2v=-2} . I have to show that the system has no solutions.. I notice that it has more unknowns than equations so it is an undetermined system.If I form the matrix ? |(2 1 3 ) (3 -1 2) (1 2 3)| I notice that the determinant is diff from zero so this three vectors are linearly indipendent. Now how do I form a matrix using ( 2 0 -2) and these three vectors with the condition that they have a determinant diff from zero? Because if they have a determinant diff from zero,the system has no solutions.
 
Physics news on Phys.org
Elaia06 said:
So I have the system { 2x+3y+z-3v=2 ;x-y+2z+v=0 ;3x+2y+3z-2v=-2} . I have to show that the system has no solutions.. I notice that it has more unknowns than equations so it is an undetermined system.If I form the matrix ? |(2 1 3 ) (3 -1 2) (1 2 3)|
I notice that the determinant is diff from zero so this three vectors are linearly independent.
Right, but what are you deducing from that?
If there are no solutions there must be a linear combination of the equations which eliminates all variables but not all constants. It's fairly easy to spot.
 
I wrote the question in the wrong way..the answer on my textbook is " The system has no solutions"..I just have to show if the system has or not solutions...
 
But if the system has no solutions the vectors forming the matrix including 2 0 -2 should be linearly indipendent /...
 
Elaia06 said:
But if the system has no solutions the vectors forming the matrix including 2 0 -2 should be linearly indipendent /...
Not sure what you mean by 'including 2 0 -2'. Do you mean the 5x3 matrix formed by moving the constants across to the left? The non-existence of solutions does not require all the equations to be linearly independent. Trivial example:
x - 1 = 0
x - 2 = 0
x - 2 = 0
In the OP, I can see a linear combination of the equations which eliminates all the variables but leaves a contradictory statement regarding the constants. That implies there are no solutions.
The det of |(2 1 3 ) (3 -1 2) (1 2 3)| is 0.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

Prove that these three ratios are equivalent
Replies
11
Views
2K
Decompose 4x4 determinant into 24 determinants -- How many are zero?
Replies
1
Views
1K
Find the solutions of the following system of congruences
Replies
2
Views
1K
Solving a system of linear equations
Replies
22
Views
4K
A gardener collected 17 apples...
Replies
32
Views
2K
Show that the system of equations has no unique solution
Replies
2
Views
874
Using Complex Conjugates to Decompose a Fraction
Replies
8
Views
2K
Constructing a 3x3 Linear system question
Replies
4
Views
2K
How to find a system of equations when the solution is given?
Replies
6
Views
2K
Find the solutions of ## 7x+3y\equiv 6\pmod {11} ##.
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top