Yo! I was wondering when solving systems of linear equations do both x and y values have the same amount of solutions? Like if x has one solution will y always have one solution too? Thanks!!
#Questions on Solving Systems of Linear Equations
hushed lintel
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Yo! I was wondering when solving systems of linear equations do both x and y val...
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tepid torrent
Yo! I was wondering when solving systems of linear equations do both x and y val...
A solution of a linear system is not just the value of x or of y, but rather a pair (x, y). Or a tuple in case of more variables.
As usual for any linear system, there are three cases:
- No solutions.
- One solution.
- Infinitely many solutions (with a certain amount of degrees of freedom).
The number of solutions can be determined by using Kronecker-Capelli theorem.
tepid torrent
No.
Again, just the values of x aren't a solution.
The solution is a pair (x, y).
hushed lintel
So (-2, 5=5/ inf many solutions) is not a solution?
tepid torrent
Sorry, don't understand what you mean.
tepid torrent
A solution of a linear system is not just the value of x or of y, but rather a p...
I can give an example of each case from here if that helps.
hushed lintel
Ik that
X= number is one solution
X = X, number = Same number is inf. Many solutions
5=/ 7 is no solutions
tepid torrent
Still not quite sure if I understand what you mean. Let me provide the examples.
tepid torrent
Here you go. In order: no solutions, one solution, infinitely many solutions (with one degree of freedom).
hushed lintel
Is the math for the first one correct?
OH WAIT I figured out a better way to ask the question
If I get inf answer for x, does that mean y also has inf answers too?
tepid torrent
Is the math for the first one correct?
If you multiply the first equation by -2, it should become -2x + 6y = -2.
tepid torrent
If I get inf answer for x, does that mean y also has inf answers too?
No. Consider the following system:
x = 0
2x = 0
Its solution is (x, y) = (0, t).
hushed lintel
If you multiply the first equation by -2, it should become -2x + 6y = -2.
oooooooo ur brain is huge for catching that thx
grave notchBOT
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hushed lintel
No. Consider the following system:
x = 0
2x = 0
Its solution is (x, y) = (0, t).
What does the “t “ stand for
tepid torrent
Ah, thanks 😅
You're welcome!
hushed lintel
No. Consider the following system:
x = 0
2x = 0
Its solution is (x, y) = (0, t).
What is the “t” in the (0,t)?
tepid torrent
What is the “t” in the (0,t)?
Parameter.
hushed lintel
I researched parameter and don’t understand why it is but in place of the “y” of the solution
I understand the 0 as the “x” though
Sorry if im not getting something
tepid torrent
If you have infinitely many solutions, you can assign some of teh variables to be parameters, then express other variables in terms of them.
The number of parameters is then the number of degrees of freedom.
The exact number of parameters depends on the rank of the system matrix and the augmented system matrix.