Matrices

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1. MATHS

FORMULA

Matrices

By

Assistant Professor (Computer Science)
Director, BST, Kokar
&
Assistant Professor (Computer Science)
‘Asst. Director, BSTI, Kokar

IIT-JEE / ENGINEERING

Buddha Science & Technical Institute
K R: 34001. arkhand, India

2. pos

ro) ops

12 Matrix: It sam arrangement of numbers in particular rows and column, Usuall it

= is denoted byZ cap eter.
E 2 Row Matrix: A matrix having only one row is called a row matrix
EM 3. Column Matrix A matrix having only one column i aed à column mat
BEM +. Square Matrix: A matrix having same number of rows and columns is called a
= square matrix. E
Es rectangular Matrix 2 à Bien TO as ot equal to number of
e columns call ctangular ma >
E à zero Matrix or Noll Matrix: À mat having its all clement erp is called zero
E mai. y NI
II 7. tae Matrix or Unit Matrix: À square matrix in which all he non diagonal
El clement ae zero anal diagonal element are one is client matrix
FEMME +. Diagonal Matrix; À Square max in which every non diagonal elements zero
= alé diagonal mate
a 9. Scalar Matrix : A diagonal matrix whose a diagonal elements are same fs called a
A scalar mari, E
EI 10, comparable Maitix: Two mars A and Bt ai o be comparable Whey Are of
the same order
11, qual Matrix 2 Two mates ar Sid o BS equal if thelr order i Same ahd the
«corresponding elements are equal

12. Addition of Matrices: Addition of matrices is possible only if the male have
same onder, The! som of two matrices is a matrix obtained by adding the
coesponding clement ofthe given mic A

1, Scale Maltpication + When 3 mi is qui by a lor mambo
lems are mu SD wih hat ie 3

14. Multiplication of Marie à The product AB of two las À and B is possible
‘onl ifthe number os columns of À requ f number of rows of.

15, Dlference of Matrices:
and.

ifierenee of matices A and Bis the sum of the matrices A

16. Transpose of Matrix : A matrix obtained by interchanging rows and columns of
matrix Ais called ranspose of matrix, Its denoted as" or A

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3. Jharkhand

ERING At Kokar, Ranchi - 834001,

M:

17. Symmetrie Matrix: A square matrix A=[u,] is said tobe a symmotrie matrix
only A'=A ie, a, =a Vi.
18, Skew symmetric Matrix + A square matrix A=[a is sad 10 be à skew symmetric

matrix if and only if A°= A à

a, Vid

19. Inverse ofa Matrix: A square matrix “Bis said tobe an inverse of matrix A AB
=BA=L lis denoted by A
20, Method to find Inverse of Matrix using elementary row transformations: Let A

be a square matrix.
Step =
Step IL + Apply sequence operations on L.H.S, and prefactors of product LA til we

write A=
set BAT
Stef The matin Bs he ered inverse of ais A. >
Note 1,0 find verse of mats A sing column operation, wits À = A
IC applying one o more clemeniarow (column) operations, Ne gall
2 ¡caros inane row (glum te A does note ANO
21. Properties of matrices : Let A; B uid C be the matrices of same order,
Wan A 4
ti) AB) CA BC) F
(i) A 402 0+ A A idan adi id or mai aii)

Au ACA) = OA) +A (in additifs)
(0) K(A+B)= KASKB, Risa ler

(0) DAS KA HA, K and tare calar &
wi) ABYC A Be), Ly y

(vi AGO) =AB+ AC

CEE
Gi (AY = A

(in (+By"
Quid Ky"
(iv) (AB)'= BA

or

KB" where K is any constant

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4. UAB = BA"
Ov) AA = ARI

ow) y="

oui ry! =A

009 ary ="

Jharkhand

22. Some Important Results +

1. Every Iemity mar sa scalar mati

2. IFAB is defined, then BA-necd nob be defincd™,

3. I both A and BER Square matrices of-same-order, then both AB and BA are
defined. (D >

4. IF ABänd BA are bo defined, it not necessry that AB = BA.
Ire product of wo macs zer) mati o bess tae of he
‘mates is ro mar.

© Aine agonal clones of symmeie matrix ae zero.

3 How any auare Ce
symmetric mati )

8, Any square mati fun Be exposed athe sum of «Smee and sk

ERING At Kokar, Ranchi - 834001,

rime maris
3) A rectangular des not posts
0 Inver a as i ish uns,

‘Note ifany mistake on this, kindly inform on the mail

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