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Matrix 1

The document discusses various mathematical concepts related to matrices, including matrix operations, inverse matrices, and properties of symmetric and skew-symmetric matrices. It outlines conditions for the existence of inverses and provides examples of matrix calculations. Additionally, it mentions the Cayley-Hamilton theorem and diagonalization of matrices.

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rajagourou
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11 views5 pages

Matrix 1

The document discusses various mathematical concepts related to matrices, including matrix operations, inverse matrices, and properties of symmetric and skew-symmetric matrices. It outlines conditions for the existence of inverses and provides examples of matrix calculations. Additionally, it mentions the Cayley-Hamilton theorem and diagonalization of matrices.

Uploaded by

rajagourou
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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MA 2O2 MATH£MATIcS- 1

UNIT T.
vomk ot aA matrix, System of linean
LInvese amd vane
Skew smmetrie and
esuahons, Symmetie,
orhogo nal matries, figen values amd Eigen
a eal matrin, chanacteeohe yuah m,
Veetws of
valueo, Cayly - Hamilton Theoren
Fro penfes of Eig2n matries]
(statment only), Diegonaliaton of
Ranle t a matix,
Invese and
transpose ot ta poduet (A8)
herem: he
te product
Dt te matrices A &BB is enal to
taken in rewwse
Brden.

sqhane matvix hem t


A io any given
2f
matin (Aji), stieu Aj ka oofaetr ot aij
in tha detrminamt IAl,
and denstal by ady. A.

ScGnned with CaMScanner


Shesronm.
matrix chen
(ady A) A
A (aj A) = |AL=
matrix
ten a matriy B is called
matrix
ovided uch
nverse ot A Àf AB- A =I
I ,

B rist. nonsingula
invse.
matix Cam hve
Note. D Bnly square
ànvese.
mabrix Can ot have
2) No- 89uau
Remank.
Lnvese of A = [wing atalve
theorm.

Rropenhas ot zh invese mahix


3
) She imverse of a mahix is wnighe y povided
it eist.

2Jhe meesy and sufient Conditim fr a


squane matrix A do Poses thi nvee io

3) Ae imvee o4 ta invee a mon-ingudan


squae mabin o thi mahis itey.
i fA]= A, povidd
19)40.
Scanned with CaMSanner
4) 2f A & B -Aingulan matris
Sroler t n AB i albo
alo nom ingular
and CAB)=k'A-!
Bperatioms f tranAposing k dnvnting
5)
5 Ahe D4
ar Commutative

iy (a) (a)
Rxampls:
O Find IA1 md adj A f A= -3
3

= I(6-3) -1 (3 +b) +i(-} -4)


= 3 -4-5 = 3-l4 -|

A2 A13
adj A = A23

A32 A33

-5)T
3
1 3

-5

3
-5
Scanned with CGMSCaNner
3 Find A
A=
-S

5 -2 2 A(aij)
Aij ofactor of
.

ttuemut

-5

To[-6+s]=

3 = 18-1s =3

Ai3 = 3 (2)+(-9(5)+ i(6) = 1


T 2

Scanned with CaMScGnner


Horne wre. Find nvese maìx.

3
A =
2

3
B= 2 3
2

-2

3
-2

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