quartz/content/Obsidian Vault/systems of linear equations and matrices..md

date	tags	cards-deck
2022-05-02		default_obsidian

#math/linear_algebra

system of linear equations

definition

#card a collection of equations that we try to solve simultaneously ! ^1651526044890

equivalent if

#card Two systems are equivalent if they have the same solution set. All solutions have to be the same. ^1651526044960

theorem

#card A system can either have:

• one solution
• no solution
• \infty solutions ! ^1651526044967

matrix representation of systems of linear equations

is it consistent?

#card/reverse a system with one or more solutions is consistent. If it has no solution it's inconsistent. homogeneous systems are all consistent, since the zero solution (trivial solution) is always an answer. in the matrix representation of systems of linear equations#reduced row echelon form, a no solution matrix will have zeroes in the bottom row, except the last column. Basically saying, "0=1". ^1652735881584