Tiêu đề Matrices & Determinants Practice Sheet HSC FRB 24.pdf ✅

2  Higher Math 1st Paper Chapter-1 5| A = (1 –2 3) [h‡kvi †evW©- Õ23] X = (x y z), B =       1 1 4 – 2 5 – 2 3 0 1 C =       (m + n) 2 m 2 n 2 l 2 (n + l) 2 n 2 l 2 m 2 (l + m) 2 (K) 3     1 2 – 1 4 + E = I2 n‡j E g ̈vwUa·wU wbY©q Ki| (L) †μgv‡ii wbq‡g BXT = AT mgxKiY †RvU mgvavb Ki| (M) †`LvI †h, |C| = 2lmn(l + m + n)3 . DËi: (K)     – 2 – 6 3 – 11 ; (L) (x, y, z) =     32 59  – 30 59  – 1 59 6| A =       2 1 1 – 1 1 – 1 3 1 2 , B =       x y z , C =       2 5 4 [Kzwgjøv †evW©- Õ23] (K) Kx k‡Z© `yBwU g ̈vwUa‡·i †hvM I ̧Y Kiv m¤¢e? (L) AB = C n‡j †μgv‡ii wbq‡g mgxKiY †RvUwUi mgvavb Ki| (M) A –1 wbY©q Ki| DËi: (L) (x, y, z) = (– 15, 7 13) ; (M)       3 – 1 – 2 – 1 1 1 – 4 1 3 7| M =     a – 5 2 2 a – 2 , N =       – 1 2 4 2 1 – 2 – 3 0 5 P =       – 2 – 2 a + b – c a + b b + c c 2 – c – a ab [Kzwgjøv †evW©- Õ23] (K) a Gi gvb KZ n‡j M GKwU e ̈wZμgx g ̈vwUa· n‡e? (L) N 2 – 5N + 4I wbY©q Ki| (M) †`LvI †h, |P| = (c – a) (a2 + b2 + c2 ) DËi: (K) a = 1, 6 ; (L)       2 – 10 – 8 – 4 4 6 3 – 6 – 8 8| 2x – y – z = 6, x + 3y + 2z = 1 Ges 3x – y – 5z = 1 [PÆMÖvg †evW©- Õ23] (K) we ̄Ívi bv K‡i      a b c 1 1 1 b + c c + a a + b Gi gvb wbY©q Ki| (L) x, y I z Gi mnM ̧‡jv wb‡q MwVZ g ̈vwUa· A n‡j A –1 wbY©q Ki| (M) †μgv‡ii wbq‡g mgxKiY †RvU mgvavb Ki| DËi: (K) 0 ; (L) 1 27       13 – 11 10 4 7 1 – 1 5 – 7 (M) (x, y, z) = (3, – 2, 2) 9| Q =       3 + x 4 2 4 2 + x 3 2 3 4 + x [PÆMÖvg †evW©- Õ23] (K)     1 – 1 2 – k g ̈vwUa·wU e ̈wZμgx g ̈vwUa· n‡j k Gi gvb wbY©q Ki| (L) hw` x = 7 nq, Q 2 – 5Q + 3I3 Gi gvb wbY©q Ki †hLv‡b I3 GKK g ̈vwUa·| (M) |Q| = 0 n‡j, mgvavb †mU wbY©q Ki| DËi: (K) k = 2 ; (L)       73 62 44 62 64 53 44 53 82 ; (M) {– 9  – 3  3} 10| A =       p p + 1 p + 1 p + 1 p p + 1 p + 1 p + 1 p [wm‡jU †evW©- Õ23] (K) we ̄Ívi bv K‡i      1 4 6 2 5 7 3 6 8 Gi gvb wbY©q Ki| (L) DÏxc‡Ki Av‡jv‡K A 2 – 7A – 8I3 wbY©q Ki ; hLb p = 2 (M) AX = B n‡j wbY©vq‡Ki mvnv‡h ̈ ‘X’ wbY©q Ki ; †hLv‡b p = 1, B =       11 10 9 DËi: (K) 0 ; (L)       0 0 0 0 0 0 0 0 0 ; (M) X =       x y z =       1 2 3 11| px + qy + rz = 1 [wm‡jU †evW©- Õ23] p 2 x + q2 y + r2 z = a (p3 – 1)x + (q3 – 1)y + (r3 – 1)z = a2 (K) cÖgvY Ki †h,     4 – 4 3 – 3 GKwU mgNvZx g ̈vwUa·| (L) DÏxc‡Ki mgxKiY ̧‡jv‡K AX = B AvKv‡i cÖKvk K‡i †`LvI †h, pqr = 1, hLb Det(A) = 0 Ges p  q  r (M) l = 1, m = 2, n = – 1 n‡j, A –1 wbY©q Ki| DËi: (M) 1 – 18       15 – 2 – 7 3 2 7 – 6 2 – 2 12| mgxKiY †RvU: tx + uy + vz = 5 [ewikvj †evW©- Õ23] t 2 x + u2 y + v2 z = 5 (t3 – 1)x + (u3 – 1)y + (v3 – 1)z = – 5 (K) M =       2 9 – 3 , N = [– 3 5 6] n‡j, [MN]T wbY©q Ki| (L) t = 1, u = 2, v = 3 n‡j †μgv‡ii wbq‡g mgxKiY †Rv‡Ui mgvavb Ki| (M) x, y, z Gi mnM ̧wj Øviv MwVZ wbY©vqK D n‡j cÖgvY Ki, D = (tuv – 1) (t – u) (u – v) (v – t) DËi: (K)       – 6 10 12 – 27 45 54 9 – 15 – 18 ; (L) (x, y, z) = (2, 3, – 1)