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

g ̈vwUa· I wbY©vqK  Varsity Question Bank Solution (HSC 27) 3 Rhombus Publications 15. hw`       1 x x 2 1 a a 2 1 b b 2 = 0 nq, Z‡e x = ? [DU 03-04; CU 02-03] – a ev b a ev – b – a ev – b a ev b DËi: a ev b e ̈vL ̈v: Option Test: x = a n‡j 1g I 2q Kjvg mgvb|  gvb k~b ̈ x = – a n‡j †Kv‡bv mvwi ev Kjvg mgvb nq bv| x = b n‡j 1g I 3q Kjvg mgvb|  gvb k~b ̈ x = – b n‡j †Kv‡bv mvwi ev Kjvg mgvb nq bv|  x = a ev b 16.       10 11 12 13 14 15 16 17 18 wbY©vq‡Ki gvbÑ [DU 02-03; RU 11-12, 10-11, 06-07; JU 11-12, 10-11; JnU 10-11, 09-10] 0 1 10 5 DËi: 0 e ̈vL ̈v: Kjvg ̧‡jv mgvšÍi avivq Av‡Q|  mwVK DËi 0| weMZ mv‡j GST-G Avmv cÖkœvejx 1.       2 0 1 3 3 3 x x 1 – x wbY©qv‡Ki (2, 1) Zg fzw3i mn ̧YK 9 n‡j, x Gi gvb KZ? [GST 23-24] 2 1.5 0.5 0 DËi: 2 e ̈vL ̈v:       2 0 1 3 3 3 x x 1 – x (2, 1) Zg fzw3i mn ̧YK, (– 1)2+1     3 3 x 1 – x = 9  – (3 – 3x – 3x) = 9  3 – 6x = – 9  – 6x = – 12  x = 2 Note: mn ̧YK = (– 1)r + c  Abyivwk 2. hw` A =     4 3 2 5 ; B =     6 1 ; X =     x y Ges AX = B nq, Zvn‡j †μgv‡ii m~Î g‡Z x I y Gi gvb KZ? [GST 23-24] 2, – 1 3, – 1 – 1, 3 – 1, 1 DËi: 2, – 1 e ̈vL ̈v: D =     4 3 2 5 = 14 Dx =     6 1 2 5 = 28 Dy =     4 3 6 1 = – 14  x = Dx D = 2  y = Dy D = – 1 3. A Ges (AT + B)C g ̈vwUa· `yBwUi μg h_vμ‡g 4  5 Ges 5  2 n‡j, C g ̈vwUa· Gi μg wK n‡e? [GST 22-23] 4  2 4  3 4  4 4  5 DËi: 4  2 e ̈vL ̈v: A g ̈vwUa‡·i μg 4  5  A T g ̈vwUa‡·i μg 5  4  A T + B g ̈vwUa‡·i μg 5  4 GLv‡b, (AT + B)C g ̈vwUa‡·i μg 5  2 (AT + B)C wbY©q‡hvM ̈ n‡e hw`,  C g ̈vwUa· Gi μg: 4  2 (5  4)  (4  2) nq| 4. 3  2 Ges 2  3 μg wewkó `ywU g ̈vwUa· h_vμ‡g A I B Gi fzw3 0 ev 1 n‡j Tr(BA) Gi m‡ev©”P gvb n‡eÑ [GST 21-22] 0 1 6 9 DËi: 6 e ̈vL ̈v: BA g ̈vwUa‡·i μg n‡e 2  2| fzw3 0 n‡j BA =     0 0 0 0 ZLb me©wb¤œ Trace = 0 Avevi, A I B Gi fzw3 1 n‡j BA =     1 1 1 1 1 1       1 1 1 1 1 1 =     3 3 3 3 ZLb m‡e©v”P Trace = 3 + 3 = 6 5. i 2 = – 1 n‡j,      i i 3 i 5 i 3 i 5 i 7 i + i3 i 3 + i5 i 5 + i7 = ? [GST 20-21] – 1 0 1 i DËi: 0 e ̈vL ̈v:      i i 3 i 5 i 3 i 5 i 7 i + i3 i 3 + i5 i 5 + i7 =       i i 3 i 5 i 3 i 5 i 7 0 0 0 = 0 Note: i n + in + 2 = 0