I appreciate the last-minute clutch Friday video to help me 4.0 my test later today.
@islamicaestheticvideos3 ай бұрын
Man this is the best "how to find range and null space " video for me. THANK YOU SO MUCH.
@retired52092 жыл бұрын
Nice tutoring. I can understand now. Thank you very much
@user-ft8io7dz2c2 жыл бұрын
Hello, David Friday, I just want to let you know that I am extremely thankful and satisfied with your elaboration on how to write a vector as a linear combination of other vectors, this knowledge will be a great addition to my skill and professional experience which further help me with my studies and professional research again I can not thank you enough for your effort on your lessons, from your best student DR.Данияр
@user-ft8io7dz2c2 жыл бұрын
true
@user-ft8io7dz2c2 жыл бұрын
shit i meant "truly*"
@raghavkumarsingh42225 ай бұрын
Iam confused in finding Range of T if T:R²-->R³...plz help
@davidfriday74985 ай бұрын
Respectfully, if you don't give me the definition of the transformation, there is literally nothing I can do to help.
@overclocked72607 ай бұрын
awesome video
@veronicanoordzee644013 күн бұрын
Your math is okay, but why don't you give a short description of the objects you are describing? Teaching is not for KZbin-amateurs.
@MrVitoCorleone2 жыл бұрын
Great
@davidmurphy5638 ай бұрын
Is this an American thing to say kernel instead of nullspace? The latter is a much better term in my humble.
@davidfriday74988 ай бұрын
Kernel applies to the transformation, nullspace applies to the matrix. The kernel of the transformation, T, is the set of all vectors, x, such that T(x) = 0. The nullspace of the matrix, A, is the set of all vectors, x, such that Ax = 0. Fundamentally, they are the same concept. The difference in terms simply lets you know if you're referring to the transformation or the matrix.
@davidmurphy5638 ай бұрын
@@davidfriday7498 I'm sure you gave a great explanation but I'm still not sure I understand the distinction. I just think of nullspace as the geometric space made by the span of all the vectors which project into the zero vector after the application of a new basis; a line, plane or whatever. Or unpivoted bases of the matrix after row reduction. Or a zero det. But listen, I self-studied this stuff so I'm not really qualified to comment on the formal stuff.
@davidfriday74988 ай бұрын
@@davidmurphy563 I appreciate the backstory of your education. If you don't understand the distinction, don't fret too much. There is a lot of vocabulary-related gatekeeping to higher level math; this is not a battle that needs to be picked. I suppose the thing to keep in mind is that a given matrix can always have a linear transformation, but a given linear transformation doesn't always have a matrix. In the first case, kernel of the transformation and nullspace of the matrix are essentially the same thing. However, in the second instance, because there isn't necessarily a matrix, the term "kernel" would be used without using "nullspace". For example, a derivative is a linear transformation, and the kernel of that transformation is any constant function. You wouldn't be able to effectively model the linear transformation of the derivative as a matrix effectively. Also, to one point you made in your reply: zero determinant is great assuming the matrix is square. However, it doesn't have to be, specifically transforming between vector spaces with different dimensions.
@captainnobody4960 Жыл бұрын
Your missing a free variable for the column with all zeros
@davidfriday7498 Жыл бұрын
The column of zeros represents the zeros on the right side of the equation. Zero is a number, not a variable. As such, no free variable is needed for this column of zeros.
@arkojyotidutta589011 ай бұрын
@@davidfriday7498❤
@matarmqds3078 ай бұрын
How i can find null (T)?
@davidfriday74988 ай бұрын
I'm not familiar with the notation you're using, but here are some possibilities: - If you mean the nullity of T, that's the dimension of the kernel of T. In this case, because of the one free variable and one basis vector, that's 1. - If you mean the nullspace of T, "nullspace" only refers to a matrix. The good news is that the nullspace of the matrix of T, which we call A, is the same as the kernel of T.