a_mnx_n+....=b_m

col=n

row=m

system has at least one solution

/

no solution

coef matrix

/

aug coef matrix

[a_mn a_m2]

/

[a|b]

same solution

row operations can make them the same

general solution

/

particular system

only variable names

/

pluged in constant to fill in other variables

homo

/

nonhomo

a=0

/

a=b

trivial

/

non

to homo

all =0

/

not all =0

Ax=B

=

A1x1+A2x2+....=B

x=variable

A=vector

linear ind

/

dep

if variables are trivial

/

not ind

unit vectors = e's

e1=[1,0,0,....]^T

e2=[0,1,0,0,0,....]^T

nonsing

/

sing

Ax=0

x=0

/

not non

invert

/

noninvert

A^-1A=AA^-1=I

/

cant

subset W

zero vector

x+y

ax

S=(w1,w2,...)

such that

W=a1w1+....amwm

dimension of the range

=rank of A^T

dimension of nullspace

null space of LT

T:v->w

range of T

v->w

null space of T

rankT+nullityT=n

shortest distance between v and plane