Free Variables in System of Equations

In this video, I showed how to identify free variables in a system of equations where there are more unknowns than there are equations.

[dasbogomil]

This video is awesome. your good mood is contagious

[kgopolomphuthi]

"FREE. Free like a bird." I'm always smiling at the aha moment when it all makes sense. THANK YOU

[realguy]

this was explained much better than the way my professor explained it.

[Aemi-run]

You're an incredible instructor. Thank you for uploading these. I'm taking linear algebra at university and this is much clearer than my textbook

[NathenZ-sw]

I am learning math to Machine Learning, and your video sealed the deal on the subject. I have been reading so much and your video simplified it, and is perfect complement for a challenging day.
Thank you!

[ludmilabolotov]

your mood is so contagious and your explanation couldn't be easier!!

[alexdefoc]

Yes that part at the end where you said it's hard to find the rank and everything after this step. It's important, learned it now!

[vishvprajapati]

Thank you, I had to see lot of vid to understand free variables and at last i found ur vid . it was such a nice exp.❤

[윈터마이-cq]

Easier to understand than lectures in my language!!

[josephparrish]

Linear algebra is so much harder than calculus! 😂

[legendaryxk]

putting sign before matrix is okay in the form u were using
i.e [a][x] = [b] ~ ax = b because product of matrix [a] & [x] is equal to matrix [b]
but if ur using augmented form [ x y | b] then seperation is needed to r emember which is the constant however it is not compulsory to use it and can be written [x y b]

[holyshit]

I have problem for you
Prove or disprove that
trace of A^m is equal to the sum(λ_{k}^{m}, k=1..n)
where λ is a scalar which satisfies following equation Ax = λx
assuming A is square matrix and x is nonzero vector
Trace of A is the sum of elements on main diagonal
Here m is nonnegative integer
I need it for justifing one thing in my video

In my opinion this problem should appear in the video series but later

[bsam]

Oga sir ! Well done sir, so is this the finally answer?

[akshatrathi]

what if I say x3 is free, instead of x4 and then x1 or x2 is free again. either way there will be 2 free variables and 2 basis variables. Is this the correct way?

[barkbarkbark]

Could I decide to make x_1 free instead of x_2? right?

[djdanzo]

why is putting = sign before the matrix incorrect?

[lifevdsongs]

Sir i think its not the final answer..i think we let the free variables s and t... and then became equation...nd then put any constant in the place of s amd t then final answer we get...

[allegry]

didnt know black people were cracked at teaching math