Examples of using Zero vector in English and their translations into Thai
{-}
-
Colloquial
-
Ecclesiastic
-
Ecclesiastic
-
Computer
What is the transformation applied to the zero vector, applied to point a right there?
And I will just make one last definition, and I will call that the zero vector.
When I take v transpose times the zero vector, v transpose is going to have k elements.
So the zero vector in Rn, if it's arbitrary, is just a vector where everything is zero. .
Linear combination of these three vectors that result in the zero vector are when you weight all of them by zero. .
And we're saying, what are all of the x's that when you transform them you get the zero vector?
But in a lot of textbooks, they will always write, oh and the zero vector has to be a member of V.
So that means that your null space of A has to be trivial, or to be empty, or to just have the zero vector.
Or another way to say that is, any v that's in our null space of a transpose A has to be the zero vector.
all the way down to xk equaling the zero vector.
It's all of the vectors in our domain, which was R2, such that the transformation of those vectors is equal to the zero vector.
Everything there, when I apply my transformation of those blue vectors, or if I take the image of my blue set under T, it all maps to the zero vector.
is x is equal to the zero vector.
x equal to zero, this says that the only solution is the zero vector is equal to the zero vector.
x2 is equal to the zero vector.
And then let's see what happens when t is equal to 0-- or r of 0; all these are going to be 0, we're just going to have the zero vector; x and y are both equal to 0--when t is equal to 1/2 what are we going to get here?
Based on that, we can say, since the only solution to Ax is equal to 0 is x is equal to the zero vector, we know that the null space of A must be equal to the zero vector.
The zero vector is a member of V, so any transformation of-- if you just put a 0 here, you will get the zero vector.
So the zero vector is definitely-- I don't care what this is, if you multiply it times 0, you are going to get the zero vector.
No vector zero there.