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12 th HACKER JUGAAD NOTES MATRICES + aie i fo Mabstix: Null_ox Zero Mafotix—> Ip all the etervents | Of radix ane equal to Zexo , then if ts fi mxn, called a null matstix and is denoted by Lrosidext Omyn Oy 0. lu "hme SQUARE MATRICES o9 76) column ‘ Rs ae. a a4 ; 7 49 nA --- On 4 As (ane Kis Qo4 O22 423--- an t “| O31 433 Oy --- Aap Afonon] = a oe ay tan (HF OY EAL nt! Gn nd Onn a then “0p 2 S744, = F — Oxdors nxn OR n “ ( 2 —rTolal Elements = n* is ; — Conjugate Elements d —*totinciple/ Lending diagonal ~j | —rNuroben of elements in uppest {atiangle 2 fr +E Oodet of Maloix : — Number of elements in lowest taiangle-* 2 2° (equal) 4+ Cofagale, Chere PES_OF_MATRICES ag Oi Row Matrix —+ A single stow malsix is ey: "a tS Qalled a stow malnix oo a dow Conjugate - Lea matrix A=@j;j3m*n is said to be row matrix, if m=1 Colurnn_Matstix—+ A Single coluren matsiix is calleda column matyix oot a column Veron «i.e - a matrix A =[aigimen is said to be column matrix ifn=1 TYPES OF SQUARE MATRICE 2. ix. —> A Squone matyix in which all the diqqoral element ate equal and all O1hex elements equal to zero is called a Sealant meabix. i. in a Scale! matstix Qij=K for p+ 7 and iy 20 pot t# "| H_ Matti fi xy — A squone mofsix in which all its diagonal Clements are equal to 1 and all ottey a:-2 rare 11y=3 elements equal fo zexo is called a 4 ie unit mataix ot identify matotix - : a= [10] Is |é°] MATRIX MULTIPLICATION | 004 (opegaTous on maraces—) matsices exists only if numbest of column of OPERATIONS ON_MATRICES firist matix is equal to the number ef sows 4. AbbITIOR_$ SUBTRACTION oF ihe second - Let A be men and 8 be nxp malaices. Then the pxoduct of matstices A and B denoted by A.B is the matsix of onde mxp whee (1-4) the elements is 01 010 Malliplicetion of Matsices —> Poicchict of tun #& Note: Congisimable foot addition | Subststaction : Osidest is same. 2. MULTIPLICATION BY SCALAR obtained by adding the products op fe Matoiy Ke Sabhi elements multiply covitespordting elements of ith sow of A and henge It ? column’ B When ?2 How 22 Roto x Colunn . EQUALITY OF TWO MATRIC 3 EQUALITY OF THO MATRICES. Amyn m4 at J Two matties Aand 8 aie said to he ‘ _ | equal ip: 3X5 8x2 Mabiix ki Matuix iy They have mn agen : =¢ Pow =f Colurnn Lepacition wise elem. off TRANSPOSE OF MATRIX equal al | A =|2 6 J o14 S Ian E> iL 6 xt 3x4 mXn 
