Page 1 :
ww N, Scanned by CamScanner, 1. Applications of Matrices, and determinants, 21 -12, 214, 2 -2 1, | -2, 8-7 3-6, 2+4 4 -1, adlja=, %3D, 2, 12-4 4-1 244, 4-1 -2-4 2+4, 9-14, 2, EXERCISE, 3-4, 8-9, 2) Find the inverse, Cif it exists) of the, following: s-RAJAN, 3 -2, DFind the adjoint of, the following:[Each 2m], -3, 6 6, 3, -5, PGIT IN MATHS, --3 4, 6, Sdn:, Let A =, 4, -3, 3 -6 6, -2, 2, aolja = [Aij], : adja = [A; 7=-3, I 3 -6|| Let A =, 3 6 6), -3 4, -2 4, -31, 9 -5, -3, 2, 6 -6. 3, 6 3 -6, -2, adja, 2 -4, -6 -3, . adja =, .adja =, -3, - 3, |A|=2+0, cii), 3, (iii) I, 3, A is non-Singular, and hence exists, 2., adgkA) = K^-' adja, 221Tadja, -2, 2, |-2 2, Let A, = (, adja, -3, =, -2 () 2, 2, -2, 3 1 2, Let A=, Aj-, 6 -6, 6 3 -6, 3 6, - (adja), A =, 3 -4, -2, | -2, 2 2, I -2, 93

Page 2 :
11, w w NI N, Scanned by CamScanner, SI RASAN, PGITIN MATIA, 24 -4 -4, 24 -4, -4 -4 24, = 2 (8-7)-3(6-2)+1(21-=CadiA), Sola:, Let A =, =2(1)-3(3)+!(9), 17 adja = [Aij]=, T24 -4, -4 24 -4, 一4 -4 24, -3 1, 9 -5-1, 2, A is non - Singular 3) If' Flax)=[losx o Sinot, an hence A' exists Show that [FGO]= F(-), bin :, Flx)=, À= Cadja), 3) If Fl)-losx o Sino, -Sina o le, 24-4, 24, 112, =5(25-1) -1(5-1)41(1-5), =(20-4-4 =112, rCosx o, Sind, 9., 6 -, -Sind, |Al = 112#0, A is non-Singular Ã, and Ā'exists, 28, 8-7 3-6 21127|F= loda o Sind, 7-6 4-3 9-14, 3-4 3-2 8-9), %3D, Sina o cosal, 3, 4, 7 2, Soln:, Let A =, +sinx Cotsinx), - cos+sinx = 1, 9, AJ-, -5, 25-1, (-5, 1-5, 3 7 2, adj a =, [AJ], 1-5, 25-1, |-5, FCOx) is non -singulas, land hence (FWJ'exists, %3D, 3 4 1, 3 7 2, -3 |, 9 -5 -1, 1-5, 1-5 25-1

Page 4 :
Scanned by CamScanner, :. AAT = I, 16) If A =, T)If A =, 3 2, 7.5, and adjAB, = [, |A1=1#0, A is non-Singulao, (adjAB) auol hence A exists, adlja =[5 -2", -8., 53, -187, B=, -3, verify that, xerify that Aladja)=(adje)A|, S. RAJAN, POT IN MATIES, = |A| I2, Soln :, AB)=BA, |ABI, Soln:, -73, 187, L 81-7, A, - -3, |A| = =24-20=4, 3 2, 13, AB=, -(adja), 5 3, 75, 5 2, !B| =|- -3, 5 -2", -7 3, -3+10, -9+4, :-2+15=13, adja = [], Aladja) = [ 8 -4, 2, -7+25 -21+10, 3 47, 58, IB/=13#0, -2/, 7 -5, 18, Bis non - Singulas anel A'=, here B'exists, AB =, -7 3, Aloolja) = [, 4 0, -, |12 35-2, 13 5--73, 2, 7 -5, 18 -11, |AB| =, BA, adljB = [2 3, adljs = ], (odjA)A =[ 347, -5-1, I (adljB), 58, -5, = -77+90=13, |ABI= 13+0, B A'S, 13 -18 7, Hrom Ofe we get, Cadlja) A:, from 0,0 and Owe uol hence (AB) exists, Alodija)= Cadlja)A = \a|I2, B, ge AB is non - Singular -1, 2, B'A, 13, -1, !A)= =15-14 = 1