period 1 anearly dependent linearly
Ay
independent
:0 non
chapterI
s e c a t i o n
.
-trivial
rectors
meltiplies trivial solution
-
homogeneous Ax trivial more weators than one
-to-one
:
Crows invertible
"=o",
entries
?
linear transformation - ò picot in
every coluamm
:TCÜtEKTYÜH+TCV)
contaims
B W
TCCû
omto yin B
3P
=EBP....
basis
)CTCû)
ifU mas
basis is a
for H if l
.i.
T each E IRM image ŞBsssbñwthem
:IRP-JIRM
Onto in of
:
any set im U with
at least one x in IRM X
3m1d.
each B IrM eigenvalue
's
on e in is the
-to-one:
image of most x in IR
^
chapter 2
inverse A
I
(080 J CAlInJ I nIAY
"
=
ad
:
-be
)
=C
,
linear transformation T ( inn
TIT fallX
TCP'7)=X'
"
:
'(X1/x
matrix Ax B B
solving
,
=
:
X
A.
=
chapter 3
Ri =
Ri + cRj :
det A =
det B
Ri
->
Rj :
det A = -
det B
Ri = <
Rj : det A =
cdet B
invertible :
det AFo
nxn matrix :
det A AT
=det
det AB = det (
AJ
Xi
rule
:
det ( cramers det A
B)
AAY der adj A
?
:A":TRetA
Area Area = det Alarea ofs
:
I
chapter 4
subspace 7. contains ò
:
closed under addition ÜB
=ÜtO
z
.
3. closed under multiplication BOC
=cû
U if it is in span E
=
.
Nul space Nul A is IR and AX
=0Y
in
^
=EX:X
:
Nul space always subspace is
?
column space COL A is the set of all linear combinations
:
.
Ay
independent
:0 non
chapterI
s e c a t i o n
.
-trivial
rectors
meltiplies trivial solution
-
homogeneous Ax trivial more weators than one
-to-one
:
Crows invertible
"=o",
entries
?
linear transformation - ò picot in
every coluamm
:TCÜtEKTYÜH+TCV)
contaims
B W
TCCû
omto yin B
3P
=EBP....
basis
)CTCû)
ifU mas
basis is a
for H if l
.i.
T each E IRM image ŞBsssbñwthem
:IRP-JIRM
Onto in of
:
any set im U with
at least one x in IRM X
3m1d.
each B IrM eigenvalue
's
on e in is the
-to-one:
image of most x in IR
^
chapter 2
inverse A
I
(080 J CAlInJ I nIAY
"
=
ad
:
-be
)
=C
,
linear transformation T ( inn
TIT fallX
TCP'7)=X'
"
:
'(X1/x
matrix Ax B B
solving
,
=
:
X
A.
=
chapter 3
Ri =
Ri + cRj :
det A =
det B
Ri
->
Rj :
det A = -
det B
Ri = <
Rj : det A =
cdet B
invertible :
det AFo
nxn matrix :
det A AT
=det
det AB = det (
AJ
Xi
rule
:
det ( cramers det A
B)
AAY der adj A
?
:A":TRetA
Area Area = det Alarea ofs
:
I
chapter 4
subspace 7. contains ò
:
closed under addition ÜB
=ÜtO
z
.
3. closed under multiplication BOC
=cû
U if it is in span E
=
.
Nul space Nul A is IR and AX
=0Y
in
^
=EX:X
:
Nul space always subspace is
?
column space COL A is the set of all linear combinations
:
.
