elementary matrices

elementary matrix

A n x n matrix E obtained from I by applying one ERO

if A is m x n, R is ERO applied to I to obtain E, then EA is

matrix obtained by applying R to A

If A is m x n and e_i ∈ Rⁿ (m x i ) then

e_i^TA = row i of A

if E is m x n, then E is invertible and E^-1 is

the elementary matrix corresponding to the inverse ERO of the one that made E

if B is obtained from A by EROs, and the EROs can be written as elementary matrices E₁, E₂, …, E_k, then B =

E_k…E₂E₁A

to get back to A from B (elementary matrices example from other flashcard)

A = E₁^-1E₂^-1…E_k^-1B

if A n x n row reduces to I, then

A can be expressed as a product of elementary matrices