Mod-01 Lec-07 Invertible matrices, Homogeneous Equations Non-homogeneous Equations

[@pyrole]

Liked the way you completed the whole circle around matrices, going from elementary operations and row reduced echelon form to invertibility and finally solving the system of equations.

[@madhurgupta3207]

at 46:50, why premultiplying Akx = 0 by A1A2...Ak-1 doesn't change the solution of x?

[@DevP-28]

awwsome...Module 1 🙌

[@anuragsri81]

Nice ...the module gives an excellent idea how to generalise the things

[@srijatobasu5349]

If A is invertible then the trivial solution is the only solution i.e. its uniqueness has to be shown for the system Ax=0

[@mr.rachetphilanthrophist601]

nicely concluded module 1

[@skrejuan_]

Thank you sir....😄

[@shreeharib9882]

is the product of elementary matrices is commutative? since we can apply operation in any order

[@RiteshArora-s9x]

No ofc not. Do for 3 by 3 case

[@hemanthnathan5342]

I finished module 1. Let's see if I can finish the other modules too

[@omgj2830]

so what do the sequence of elementary row operations on A inverse result in?

[@yash9shhreya]

omgj you will get (A^-1)^2

[@yash9shhreya]

(A^-1)^2=E_l E_(l-1)...E_(1) (I *A^(-1))