Examples of using Null space in English and their translations into Arabic
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Colloquial
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Political
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Ecclesiastic
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Ecclesiastic
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Computer
And this is our null space.
Your null space will always, at minimum, contain the 0 vector.
So this will be some special member of your null space.
So the null space of this matrix is the eigenspace.
Well the solution set of this is just the null space.
That means that the null space of this matrix has got to be nontrivial.
Where this guy right here is a member of the null space.
They're the exact same null space, the exact same solution set.
We call this right here, we call n, the null space of a.
The null space is just the 0 vector, this part of your solution disappears.
In this case, we will calculate the null space of matrix A.
By definition our null space is all of the x's that satisfy this equation.
Plus some homogeneous solution, so some member of the null space.
The null space of the set is the set of vectors created from the free variables of the system.
But in this video let's actually calculate the null space for a matrix.
So the null space of B was equal to the null space of the reduced row echelon form of B.
Let's say I have this matrix B, here,and I want to know what the null space of B is.
The null space is the set of all the vectors, and when I multiply it times A, I produce the 0 vector.
I can pick any combination here to create this solution set,or to create our null space.
You remember how I told you that this null space bubble that we're in was not much larger than the station?
All the potential x1's through x5's or all thepotential vectors X right here, that represents our null space.
In the last video, I spoke somewhat theoretically about what a null space is and we showed that it is a valid subspace.
The null space of the reduced row echelon form is the same as the null space of our original matrix.
If all of these guys are linearly independent, then the null space is just the 0 vector.
So we can write that the null space of A is equal to the null space of the reduced row echelon form of A.
Or we could say that the eigenspace for the eigenvalue 3 is the null space of this matrix.
This guy's null space is going to be the null space of that guy in reduced row echelon form.
So you can say that x minus-- so our any solution x minus the particular solution of xis a member of our null space.
And we have done this multiple times butjust as a review, the null space of B is just all of the x's that are a member.
And then we determined, look the only way that this is going to have a non-zerosolution is if this matrix has a non-trivial null space.