Title Matrices Varsity Question Bank Solution (HSC 27).pdf ✅

g ̈vwUa· I wbY©vqK  Varsity Question Bank Solution (HSC 27) 1 Rhombus Publications weMZ mv‡j DU-G Avmv cÖkœvejx 1.         bc 1 a a ca 1 b b ab 1 c c =? [DU 24-25] 1 0 1 2 abc DËi: 0 e ̈vL ̈v:         bc 1 a a ca 1 b b ab 1 c c = 1 abc      abc 1 a 2 abc 1 b 2 abc 1 c 2 =       1 1 a 2 1 1 b 2 1 1 c 2 = 0 [⸪ `ywU mvwi GKB] 2.       1 2 1 3 0 – 1 2 3 p g ̈vwUa·wU e ̈wZμgx n‡j, p Gi gvb KZ? [DU 23-24] 4 3 3 4 5 3 3 5 DËi: 4 3 e ̈vL ̈v: e ̈wZμgx n‡j,       1 2 1 3 0 – 1 2 3 p = 0  1(0 + 3) – 3(2p – 3) + 2(– 2 – 0) = 0  3 – 6p + 9 – 4 = 0  8 – 6p = 0  p = 8 6 = 4 3 3. A =     1 2 2 5 n‡j, det(AA–1 ) Gi gvb KZ? [DU 21-22] 1 – 1 0 – 1 2 DËi: 1 e ̈vL ̈v: AA–1 = I [I n‡jv A‡f`K g ̈vwUa·]  det(AA–1 ) = det(I) = 1 Note: A‡f`K g ̈vwUa‡·i wbY©vq‡Ki gvb 1 4. hw` A, B, C g ̈vwUa· wZbwUi AvKvi h_vμ‡g 4  5, 5  4 Ges 4  2 nq, Z‡e (AT + B)C g ̈vwUa·wUi AvKvi wK? [DU 20-21] 4  2 5  4 2  5 5  2 DËi: 5  2 e ̈vL ̈v: B g ̈vwUa‡·i μg 5  4  A T + B g ̈vwUa‡·i μg 5  4 C g ̈vwUa‡·i μg 4  2  (AT + B)C Gi †ÿ‡Î, (5  4)  (4  2)  (AT + B)C Gi μg: 5  2 5. A =     3 2 – 4 – 3 n‡j, det(2A–1 ) Gi gvb n‡jvÑ [DU 19-20] 1 4 – 4 4 – 1 4 DËi: – 4 e ̈vL ̈v: |A| =     3 2 – 4 – 3 = – 9 + 8 = – 1  det(2A–1 ) = 2 n |A| [†hLv‡b, n gvÎv] = 2 2 – 1 = – 4 6. A =       a – 2 – 5 2 b 3 5 – 3 c GKwU eμ cÖwZmg g ̈vwUa· n‡j, a, b, c Gi gvb ̧‡jvÑ [DU 17-18] – 2, – 5, 3 0, 0, 0 1, 1, 1 2, 5, 3 DËi: 0, 0, 0 e ̈vL ̈v: AcÖwZmg/wecÖwZmg/eμ cÖwZmg g ̈vwUa‡·i †ÿ‡Î gyL ̈ K‡Y©i mKj fzw3 0 nq| 7. k Gi †Kvb gv‡bi Rb ̈      1 1 1 1 k k 2 1 k 2 k 4 wbY©vqKwUi gvb k~b ̈ n‡e bv? [DU 17-18] k = 1 k = – 1 k = 3 k = 0 DËi: k = 3