Examples of using A matrix 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 hopefully you're satisfied that a matrix multiplication, it isn't some new, exotic form of transformation.
Remember, even though I have a matrix vector product right here, when I multiply a matrix times this vector, it will result in another vector.
Now, I just told you that I can represent this transformation as a matrix vector product.
But anyway, back to our attempt to represent this transformation as a matrix vector product.
We have more columns here than entries here, so we have never defined a matrix vector product like this.
We know this guy is a linear transformation, in fact that's one of the conditions to be able to represent it as a matrix.
And we also said that every linear transformation we have shown in a previous video, can be represented as a matrix.
What I'm going to do in this video is introduce you to a new type of space that can be defined around a matrix, it's called a column space.
So, so far we started off with a matrix-- I will do it in purple-- we started off with a matrix a is equal to a, b, c, d.
Sal, I already knew how to-- in algebra II in tenth grade or ninth grade, I already was exposed to multiplying a scalar times a matrix or adding two matrices with the same dimensions.
And if the transformation is equal to some matrix times some vector, and we know that any linear transformation can be written as a matrix vector product, then the kernel of T is the same thing as the null space of A. .
What's the span of a matrices' column vectors?
So, that equals A, matrix A, plus the matrix, we just multiply the negative one times every element in here.
This is not a matrix.
And excreting a matrix of conscious frequencies.
You can write all of those as a matrix.
How do you find the determinant of a matrix?
Well, this is a matrix.
We once again reduced everything to just a matrix multiplication.