:Lineas Atgebra:
2 Definatfon of Matrx:
into the fom ot
A system ot mxn numbers arrangea
an
Tectangulr array havi ng m rowS Rn columns s called
matrix ot order
OYder mxn
12-
ik A-[aij]=
a22 agn
am1 Qma amn
HoriZonta) lnes are caled rous verHcal Line are caled colunns.
SofuQe Matrix:
An n matrix fo which m=n is called syuare matrix.
The elem entsnts ait::
aiti ii, e Gua22, a32 CLre ealled
elemets di agno elements the 1Pne along which it they lie
is called Prin ciple diagonal ot matnix.
Elements other than al Qy etc ae called off -diagon
elements i,e aiilij:
oDiagonal Matrix:
A sauare matrik in which all off diagnal elements are
~oro is called diagonal Matr. The diagonal elements
may or may not be Zero a i =o ititt
ait if i-j
, 03 3 3
matsa scalan a
=A
=j i if K =aij
i+Í if o =aif
eoal. being eloments
dagoa all with matix diagenal a matnk
is Scalar A
Matrix: ScalaY
3]=*1 diag
=|La 2] Ca,9, aiaDeterminat
g ot vi)
of
valves Eign Vy
i)
efties. Prop A
) 5L3diag = Awriten
as
bel oals can matrix.
It diagonal a is
A=
3
, Unit matux or Ldentity Matin
ASafuae matin A-Laji] is a wnit matk it aij =1
when aH =1 When i=j k aj =0 when i +] S aH =o if
i+
aij =1 if (-j
1
is a nit mot.
1
A Properties:
9 I is Ldenttty eements fx multiptication.
) I" I
dy I-! =I
(e) (I| =1
Null Matrix:
Null matrix is denated by 0. NUl
matrix need not to be sauase
CLif otij
A Propeties ot Null Matrix:
) Ato =o+A =A
So G6
66
o is addi tive identity 99
(b) A+ CA) =o
2 Definatfon of Matrx:
into the fom ot
A system ot mxn numbers arrangea
an
Tectangulr array havi ng m rowS Rn columns s called
matrix ot order
OYder mxn
12-
ik A-[aij]=
a22 agn
am1 Qma amn
HoriZonta) lnes are caled rous verHcal Line are caled colunns.
SofuQe Matrix:
An n matrix fo which m=n is called syuare matrix.
The elem entsnts ait::
aiti ii, e Gua22, a32 CLre ealled
elemets di agno elements the 1Pne along which it they lie
is called Prin ciple diagonal ot matnix.
Elements other than al Qy etc ae called off -diagon
elements i,e aiilij:
oDiagonal Matrix:
A sauare matrik in which all off diagnal elements are
~oro is called diagonal Matr. The diagonal elements
may or may not be Zero a i =o ititt
ait if i-j
, 03 3 3
matsa scalan a
=A
=j i if K =aij
i+Í if o =aif
eoal. being eloments
dagoa all with matix diagenal a matnk
is Scalar A
Matrix: ScalaY
3]=*1 diag
=|La 2] Ca,9, aiaDeterminat
g ot vi)
of
valves Eign Vy
i)
efties. Prop A
) 5L3diag = Awriten
as
bel oals can matrix.
It diagonal a is
A=
3
, Unit matux or Ldentity Matin
ASafuae matin A-Laji] is a wnit matk it aij =1
when aH =1 When i=j k aj =0 when i +] S aH =o if
i+
aij =1 if (-j
1
is a nit mot.
1
A Properties:
9 I is Ldenttty eements fx multiptication.
) I" I
dy I-! =I
(e) (I| =1
Null Matrix:
Null matrix is denated by 0. NUl
matrix need not to be sauase
CLif otij
A Propeties ot Null Matrix:
) Ato =o+A =A
So G6
66
o is addi tive identity 99
(b) A+ CA) =o
