Examples of using Solution set in English and their translations into Thai
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Colloquial
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Ecclesiastic
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Ecclesiastic
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Computer
Well the solution set of this is just the null space.
Or if we wanted to write the entire solution set, it would.
What is the solution set to the equation of Ax equal to 0.
we're looking for the solution set to that.
You get an equation-- you get a solution set that looks something like that, and you call that your null space.
We set it and then that's going to be x3 in our solution set. x4 is not going to have any x3 in it.
You're going to have your-- let me write it like this, your solution set is going to be equal to some scalar multiple.
The solution set for this guy right here, for this first equation right there, is going to be x1, x2 is equal to what?
Which means that it is essentially impossible to find an intersection of these three systems of equations, or a solution set that satisfies all of them.
But this guy right here has to be-- for any solution set, depending on how you define it, there's only one particular vector there.
What you can imagine is, is that the solution set is equal to this fixed point, this position vector, plus linear combinations of a and b.
then our solution set is going to the vector 0,
Or put another way, the solution set of this equation, which is really just a nullspace, the nullspace is all of the x's that satisfy this equation.
So if you pick a particular b right there that has a solution, we just said that everything on this line will map to that point in our solution set.
The solution set to any Ax is equal to some b where b does have a solution, it's essentially equal to a shifted version of the null set, or the null space.
So what we can do is, we could say that all the solution set here is equal to the vector 1, here, so now we have 1 plus minus 3 times t for x1.
And then when you un-augment-- when you create the system back from this right here, because these two systems are equivalent, you are essentially going to have your solution set look something like this.
Your solution set that satisfies this is going to be, x is going to be equal to this b prime, whatever this new vector is, this b prime plus something that looks exactly like this.
So if I wanted to write the solution set to this equation, if I wanted to write it in terms of this, I could write x1, x2, x3, x4 is equal to-- what's x1 equal to?
And if we want to write our solution set now, so if I wanted to find the null space of A, which is the same thing as the null space of the reduced row echelon form of A.