Linear Algebra - Lecture 17 - Matrix Transformations

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Who is here before a Math exam 😂

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2 minutes before one, as a matter of fact.

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@@shanemcphillips4070curious,how was it?

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Here ,i'm😅

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You caught me

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I am on a revision spree of Linear Algebra. Your lectures are really lucid!

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you saved my grade dude! i appreciate it!!! no other tutorial was as concise as yours!!

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I owe you so much right now. Thank you, from Florida.

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You read my mind on the exact things I was confused about. Thank you so much.

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Thank you sir
The complex idea has been turned to a simpe concept 😊

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this is soooo helpful!!
I wish I have u as a professor!

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Thank you Professor Hamblin.
I'm a U-Toledo student. Some quality last moment cramming here. ☻

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That profile picture is against Islam and God!

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Allah created Linear Algebra, he created math, he created you! So to disrespect him is to disrespect all his creations

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Riiiiight lol

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Thank you so much for your lectures, easy to understand and straight to the point

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His explaination is just wonderful.

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Great easy-to-understand lecture! Thank you!!!

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Straightforward and Detailed

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I wish you could explain Tensor Algebra as well because it is a cause for my desperation!

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Ur lecture is grt man 🔥🔥

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Thank you for this. Much appreciated.

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wow ...thank you alo @James Hamblin

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Outstanding explanation 👍

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[@JBLTALK]

I got lost at the row reduce part

[@mirzaabdurehman3539]

hhh me too

[@xoppa09]

the range of a transformation is a subset of the codomain

[@HamblinMath]

True

[@Komal-Sutar]

Thanks a lot, from India. 😊

[@jvc_1]

Thank you so much,
please can you explain row reduction

[@HamblinMath]

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Hello your lectures are so great , You're a savior

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Thank you soo much

[@dudius3743]

how was our row reduction different between b & c? wouldnt they have the same answer?

[@HamblinMath]

The two vectors are different. There's a -5 in the "b" vector and a +5 in the "c" vector.

[@dudius3743]

thanks, I missed that lol @@HamblinMath

[@sakcee]

@HamblinMath do you have pdf of the slides? thanks

[@HamblinMath]

You can find the full textbook here: webspace.ship.edu/jehamb/ela/

[@sakcee]

@@HamblinMath Thank you!, you have excellent teaching skills and very intuitive teaching style!

[@detree]

Wdym pivot in the last column

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tnx u so much

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All Imma say is: 👑

[@sandeepneemkar]

How can we geometrically interpret that its not in range of T? I mean how to visualize the vectors whose transformation falls out of range of T?

[@muhammadbasit6176]

Helpful

[@ColyneOwino]

Good

[@elinanikolopoulou1769]

T(x) is the image or the transformation ?

[@HamblinMath]

T is the transformation. If x is a vector, then T(x) is the image of x. Sometimes we'll refer to the transformation as "T(x)" (where x is just a generic variable, not a specific vector). This is similar to when we refer to a function as f or f(x) interchangeably.

[@Ary2345]

In simple words for image when you solve T(X) = Ax the thing you get as a result is the image .

[@nealdyxthercentino5576]

From the example 2:00, why is it R3 to R2?

[@jensmalzer6344]

Because the matrix is 2 x 3, you go from R3 to R2.
So basically for an m x n matrix, you go from Rn to Rm

[@confused6526]

I wonder why mathematicians decide to use many jargons which refer to the same shit? Domain -> Codomain... is the same as ... Image -> Range.... T refers to f which is a function....
Heck....

[@HamblinMath]

As explained in the video, domain, codomain, image, and range all refer to different things. It is important to use precise language so that our meaning is clear.
Since transformations are a special kind of function, we often (but not always) use "T" since it is the first letter of the word "transformation."

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