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For the row space, it's the transformed rows in the Reduced Row Echelon Form (those with the leading 1's) that you use, because they are the clearest and simplest representation of the linearly independent vectors that span the row space of the original matrix. You cannot use the rows of the original matrix corresponding to the pivotal rows in the RREF to form the row space directly. Here's why: When you perform row operations to transform a matrix into its row reduced echelon form (RREF), these operations generally alter the original rows. While these operations preserve the row space itself (meaning they don't change the set of all possible linear combinations of the original rows), the specific rows themselves are usually changed.

Thankyou ❤❤

Hernandez Mark Taylor Gary Martin Ruth

I want to study.

Thank you

These is very helpful . Thank you bro

Good lecture method

Thank you sir for the knowledge shared.

What you wrote was Ut = kUxx which transforms to become Ut - kUxx = 0. This looks like the diffusion equation

Please it looks like this is rather the diffusion equation or.... The heat equation is of the form Ut = c^2Uxx

Perfect!

Thnxx sir

thank you

Not everyone gets to watch all the previous videos so please do everything .

Thanks bro

Do u have more pde videi

كل التوفيق إن شاء الله 💙

nice

speak more clearly

First to comment which screen recorder and whiteboard are u using Boss

Why did you expand it on a half range yet it's from 0 to 2l which indicates a full range

Also from my side, cannot express the amounts of thanks given. Indeed.

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thank you so much sir 🥰you just save me 😇😇😇

12:52

thanks

Boss please which screen recording and board are you using

Great

Thanks alot boss

C^2=3 why

Great work...very comprehensive

""If a fn. satisfies CR eqn. it does not imply fn. is analytic"". counter : f(z) = (|xy|)^(1/2) satisfies cr eqn at (0,0) but not differentiable hence not analytic. but since all partial derivatives are continuous in the examples taken therefore these examples are analytic also. thank you

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Why do we choose t to be equal to x

Thank you Sir 🙏

this guy makes too many mistakes its hard to follow at times

Thanks I appreciate i understood

The background noise was very annoying, so that I could not continue watching😔

The Determinant of the first matrix should be 16.

Thank you so much. It was much needed, Sir.

so sweet continue doing good

I have been able to use the simpson’s 3/8 to solve thank you

Could you please post solution for type 2 with derivative BC

God bless you bro. You made my day

Lifesaver sir, thank you so much!

k is the number of columns in the first matrix and the number of rows in the second matrix. I interchanged them when saying it.

Mexams taught me in 1st year @KNUST, he was a TA then, and he’s the best i’ve seen…so far

finally got the video of bounds of eigen value

What if the terms dont all cancel out at the end, when you plug in the partial derivatives of u back into the original equation?