Question

2 . a b с d 3х a р 9 7 Let det S 9 and C= u - 4x -p 2v-8y -29 K-41 -S x 6y 26 3t d y 7 2 are given. N 21 ין w k W - 42 -1 32 с Calculate det(3C-1)

Answer 1

hiven; det a b P 9 y oln 2 r s z t u V W K 3a ca u- 4x 2v-dy kadt - 29 by ab 3t d - r W- 92 с N To find! det (30-1) 2 Solni Let A = a b P 2 S al y on 3 2 t u v . det (A) = 9 2 Now 3x a U- 4x 20-84 k-qt 69 - 2.9 -s ono 3+ 32 W - 42 с Taking common factor 2 from R2, we get: C - 2 3n ܩܢ U-&x V- 4y K-4t W - 42 - -S 34 3t d 32 operating c, yete3 we get :

C - 2 -P -2 U-axton V - dy+3y K-4t+3+ W-42 +32 Зи 34 3t b d с a C - 2 U-x V-4 b ! ( [ 30 3 y 3t 32 ol W- 2 Taking factor of 3 from column 3 (C3) we get - 2x3 -q U-x vy kat W-2 9 t a b d c -s 2 cu 6 u-n V-y NT as a b d W- 2 operating c citez we get а C C 6 - q x y t -S ठ z we get Transposing c CT = 6 k -s - r q y t 2 b C operating R Ra i we get 1

T СА b с d - S + - 9 y 1 2 u V k - a + 2 Taking (-) sign from R2 we get b ol с CT = (-6) P 1 S r "X y u V K operating - Ca we get c T = (-6) b с d q h S 9 2 t V - om o a x J K 3 CT = (-6) letl=101 = (-6) 1 A1 = (-6)* 9 = -27 (0) > Now, cal 12 adj c 10) adj c -27 el=-271 -27% 36 - 1 - 1 - 1 adjc 9 :. 130-11 - 1 / 2 (adje | Sladj c ) 2 . Elcin-) 4-1 - 1 ling - lelon (27) 3 - 2187