Examples of using Any vector 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
So let me just write any vector.
I can pick any vector in R3 for my a's, b's and c's.
And S is equivalent to A times any vector in.
You can give me any vector in R3 that you want to find.
I just told you that I can represent any vector like this.
That tells me that any vector in R2 can be represented by a.
But you can clearly represent any angle, or any vector, in.
If I take the length of any vector, I will do it here.
Any vector in our left null space can be represented this way.
Now, can I represent any vector with these?
I can take any vector in Rn and it will map it to some factor in Rm.
We can now rewrite this transformation here as the product of any vector.
And that's true for any vector that we pick that actually.
So any vector that's in our column space could be represented this way.
But now I can represent any vector in r2 as some combination of those.
I want to give you the sense that it's the shadow of any vector onto this line.
But any vector here in R3 I will be rotating it counterclockwise around the x-axis.
And you might remember, the magnitude of any vector is kind of a Pythagorean theorem.
So any vector in the plane dotted with my normal vector is going to be equal to 0.
Orthogonality, by definition, means its dot product with any vector in I is 0.
You have to be able to get any vector here with a linear combination of these guys.
If you just sum these guys up in multiple combinations, you can get any vector up there.
This just means that I can represent any vector in R2 with some linear combination of a and b.
Now, the neat thing about this identity matrix becomes evident when you multiply it times any vector.
You can represent any vector in your subspace by some unique combination of the vectors in your basis.
But because these are the exact same direction, you can't get to any vector that's in a different direction.
Which means that any point, any vector, in your two-dimensional space can be represented by some combination of those two.
EPS vector file, which can scale to any size and be opened with any vector program, like Inkscape which is free.
So we now know that our normal vector 5, minus 1, minus 1, that I got by taking the cross product of our basis vectors dot any vector in our plane.
You can construct a unit vector that goes in the same direction as any vector, essentially just by dividing, or I guess multiplying, that vector times 1 over its length.