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hello...so for the circle r(1,r) and (-1,r) do you choose an abitrary radius for them?? or how do you determine their radius

Dr. Incognito, you rock..thank you!

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Thank you!

What do we do in case we have two different unknown values? f(x,y)=.... ?

is your last name actually incognito?

Interesting fact: The null space of a matrix is a subspace of Rn and the column space of a matrix is a subspace of Rm with the matrix being defined as m x n matrix. This tells us that the null space of a matrix is a subspace of Rn or the number of columns and the column space is a subspace of Rm or the number of rows. That is why the null space has the same number of entries as the amount of columns while the column space has the same number of entires as the number of rows is what he is trying to say. Basically Dim(colA) = number of pivot colums and dim(nulA) = number of free variables, thus number of pivot columns + number of free variables = total number of columns

Ah perfectly explained, tyvm

Your video was a big help, thank you!

best video about row space so far.

Hey Dr. Incognito -- I'm a high school student that stumbled on your videos by serendipity, but you're helping me get through my linear class! Your videos are much more comprehensive than any others I've found :)

Really helped me!!

thank a lot Dr. incognito :D

Thanks for the clear explanation! Still a bit unclear about certain stuff, but this certainly did help :)

Oh yes because exponentials are never equal to zero.. But I can't solve this question with your method.. Can u help? Qns: Is y=3e^-2x an increasing or decreasing function?

Why can't we use the exponential e^-x in the last example to obtain our x values? Can it be used?

A good explanation, clear and concise, but you need to turn off the cameras auto focus as it's distracting. Cameras find focus by contrast so if you have a plain colored surface like a whiteboard it will be difficult for the camera to know where to focus. Set it manually and then turn it off.

Thank you, I was waived into Calc 1 and your resources along with Dr. Dahal have been extremely helpful .

His wardrobe is boring.

you are the best sir. i learnt most of linear algebra in 3 days partly because of you

u r carazy good man

Epic. You made it easy for me. Thanks.

Wow very informative, clear, simple and understandable! Thank you so much.

I heard the grudge

keep up the hard work man! good video.

Not sure if Incognito is actually your name, but if it's not, it's great! This is a great series. It's actually quite a bit better than the more popular math-help videos.

Great explanation, its I was finding it hard to reconcile both these concepts side by side until i heard this.

Thanks a lot for the very clear explanation. Helped me a lot :)

Easy to follow, thanks!

Great example, thanks for sharing.

Thank you so much for your video. It really clears my doubt

Just what i needed , Thanks a lot

Good video real explanatory thanks

nice video, very helpful. thanks!

Amazing thank you!

but i was actually looking for a video on orthogonal complements of an inner product subspace..

great lecture! explained so many things that my prof didnt emphasize!!!!! Thank you Dr. Incognito!

VERY useful, thank you! It saddens me this has got such a little amount of views, its a great thing that you upload these lessons for free for everybody This is a very clear and concise explanation :)

Good explanation, odd name...

I agree. thanks for posting this. Really cleared things up for me.

x = 2 at the end, not 1 :)

@themrdaydreamer Since the numerator can have degree one less than the degree of the denominator (but not more), we must make sure that each of our partial fractions has that same property. Otherwise, there would be some fractions which we would not be able to decompose.

I LOVE YOU

please invest in a headset. You are a good teacher, but this vid needs an audio boost!

Thanks. That explanation helped out a lot.