Vypočtěte determinant pomocí úprav a Laplaceovy věty. Evaluate the following determinants by row operations and Laplace theorem. Poznámky: a) vytknutí, b) Laplaceův rozvoj podle nejvhodnějšího sloupce nebo řádku. Comments: a) we take out some number(s), b) we expand determinant along some row or column. 1 \2\ 3 4 -10 3 4 0 0 3 4 -1 -2 -3 4 12 3 4 -10 3 4 0 0 3 4 0 0 0 8 a) 2-3-4 1111 -10 11 0 0 11 0 0 0 2 b) 24-2-(-1)4+4 1 1 1 -1 0 1 0 0 1 48 • 1 = 48 2 0 S 4 1 -4 0 3 -3 3 3 -1 8 0 -1 2 9 5 3 -1 5 1 1 2 b) l-í-l)^1 -8 -9 5 -8 5 1 3 -1 2 0 -14 4 -8 5 1 = - m -1 2 -14 4 -4 3 -1 2 294 E o 3 -1 3 -4 -2 3 0 -3 -1 9 -4 17 3 -8 b) l-(-l)1+1 -1 9 -4 17 m -s -1 9 -7 ED 9 -5 3 -8 1 0 0 -1 9 0 19 -2 -5 -14 38 0 2 -2 2 -3 2 1 -8 b) ■l-(-l)1 + 1 -2 4 3 -3 6 5 1 -6 -2 -2 4 3 R| 0 3 1 -6 -2 4 0 -6 b) _l.4.(_l)l+2 0 2 -2 2 -2 2 3 -8 0 2 1 -2 4 3 -2 8 6 3 4 3 b) ("l)-(-l)1 + 1 -2 4 3 -2 8 6 3 4 3 a) -4-3- -2 1 1 -2 2 2 3 1 1 2 3 2 [3] 3 4 4 4 4 2 3 4 12 2 3 2 2 1 2 10 3 2 3 1 2 1 -i E i -1 1 -1 5 0 3 0 -1 1 0 0 b) 1. (-1)3+3 -2 5 -3 3 8 0 2 5 1 3 3 -1 = 2- 4 0 2 5 -7 3 4 0 b) 2 • (-1) • (-1)3+3 2 5 -7 3 -82 1 2 3 -5 3 1 2 -3 -5 3 1 -3 - -5 3 8 2 2 -2 0 2 2 2 -2 4 U 1. (-1)5+5. 8 2 2 -2 ^2 •2- 4 1 1 2 2 2 -2 1 1 1 5 -4 -7 5 6 -5 -4 - 7 5 -5 - -4 -7 0 0 0 -2 0 -4 1 4 0 -2 -4 4 = 4- 3 1 0 1 0 1 0 -1 bJ4.(-l).(- _l)3+4 . 3 0 0 bJ4.3 (_1)2+1 0 1 - -2 0 1 — 2 0 -12 4) = -48 2 1111 0 -5 -1 -1 -1 0 3 111 1 3 111 114 11 = 0 -2300 1115 1 0 -2040 11116 0 -2005 = -1 • (-2) - (-1) - 5 10 1 -2 3 0 0 10-20 = -2 0 0 5 _c -1 -1 -1 b=h • (-1)2+1 • -2 3 -2 0 0 0 4 0 -2 0 0 5 5 111 -2- -2300 11 2 0 2 bJ-2 l-(-l)1 -2 0 0 5 -2 • [-20 - 12 - (165)] = 394 0 1110 0 1111 12 3 0 0 0 12 3 0 0 0 12 3 1 1 1 0 1 1 0 1 2 0 1 2 0 0 1 1 0 1 1 -1 0 3 0 2 3 b) l-(-l)1 + 1 1 1 1 2 1 2 0 1 1 E -1 0 3 0 2 3 1 1 1 2 1 2 -3 -2 l-í-l)^4 i -3 2 -1 2 3 = - 2 -1 1 2 -1 0 0 4 0 4-4 16 10. 3 1111 0 2 111 113 11 1112 1 2 2 2 3 4 -5 -2 2 1 -1 2 -1 0 -2 0 b) l-í-l)^1 -2 -2 0 0 1 0 1 0 -7 -2 -1 2 -1 0 -2 0 -1 0 0 0 1 0 1 2 b) .1. 2- (-1)4+4 7 -2 -1 ^ 1 2 0 ^2- 1 0 1 7 2 1 -12 0 -1 0 0 8 2 0 1 2 0 b=h. 8 2 -1 2 1 0 1 36 11. 2 3 3 4 1 3 4 12 1 2 12 6 3 4 4 1-13 2 0 0 2 0 0 b) 2. (-1)5+3 2 3 4 E 2 3 4 1 3 1 4 2 1 3 2 4 = 2 -1 -7 -2 -10 -7 -13 0 0 4 1 3 2 0 -5 -5 0 b) 2-l-(-l)i+4 -1 -2 -7 -10 0 -5 -7 -13 -5 -2 • (-1) - (-1) - (-5) 1 2 7 i -5 7 10 13 = 10 7 -3 0 i E 0 1 10 • 32 = 320 12. 0 e o 1 o 1 0 3 2 7 0 9 3 7 0 27 4 3 0 3 0 6 0 10 1 0 8 4 0 1 0 1 1 3 0 7 3 9 0 0 3 27 0 -4 7 b) 1. (-1)2+2 12 0 3 0 14 0 9 0 3 1 [T] 0 3 18 0 27 0 4 1 2-4 7 2 0 3 0 4 0 9 0 11 0 3 8 0 27 0 -10-4 1 b) 1. (_l)3+3 2 3 0 4 9 0 8 27 0 -1 -4 1 b) 1. (-1)4+4 E 2 3 1 4 9 1 8 27 1 2 3 0 2 6 0 6 24 12 13. QO 0 0 7 0 3 7 0 0 7 3 0 7 0 0 3 3 0 0 0 3 7 0 7 3 4 0 0 a) 3 0 0 0 3 7 0 7 3 E 0 0 0 0 0 10 0 3 7 0 0 7 3 0 Q] 0 0 -1 b) 4-l-(-l)4+i 0 0 10 3 7 0 7 3 0 b) (-4)-10-(-l)1+3 3 7 7 3 40 • (9 - 49) = 1600 14. 11110 i i o i Q] 2 3 10 0 12 0 3 0 0 10 2 3 1110 10 11 3 10 0 2 0 3 0 -2010 b) 1. (-1)2+5 i E i 3 1 0 2 0 3 -2 0 1 (-1) 1 1 1 1 2 0 1 2 0 -3 -2 0 b) (-l).l. (-1)1+3 E 2 -1 i 2 3 -3 -2 1 (-1) 1 2 -1 0 0 4 0 4 -2 (-1) • (-16) = 16 15. 0 4 1 1 7 -2 -13 2 -4 2 3 -1 4 0 -2 7 0 3 -4 -1 2 10 1 7 10 -1 -2 7 3 -4 2 10 7 10 0 -2 0 0 15 0 -5 0 -10 0 4 1 -2 7 1 1 3 0 4 3 0 5 17 0 b) 1. (_l)5+5 b) 5-(-l)i+3 -2 7 1 3 -4 -1 2 10 1 7 10 -1 1 4 5 3 3 3 EU 17 -2 0 15 -5 -10 4 13 12 O 4 3-1 -3 11 O b) 5-(-l)-(-l)2+3 13 12 -3 11 5 • (143 + 36) = 895 16. 5 6 0 0 0 Q] 5 6 0 0 0 15 6 0 0 0 15 6 0 0 0 15 -19 5 1 0 0 -30 0 0 6 0 0 5 6 0 1 5 6 0 1 5 b) (_1)2+1 -19 1 0 0 -30 0 0 5 6 0 1 5 6 0 1 5 (-1) -19 1 0 0 -30 0 5 0 1 0 0 1 o -30 -19 5 b) (-1) - (-l)4+3 -19 1 0 30 0 5 -30 = 1 -19 -20 1 0 -35 5 1 4 7 -6 ^ 1 5 -30 = 5- 0 1 -19 4 7 6 [I] 5 30 = 5- 0 1 19 -13 -114 5 5 1 19 b) 5-(-l)2+1 -13 1 -5-(-13-19+114) = 665 17. E 0 -1 1 1 0 -1 1 0 1 1 1 0 1 1 1 a b c d 0 b c + a d- - a -1 1 1 0 0 1 0 1 b) 1 1 b a + c E o 0 1 0 c + a 1 0 18. 19. 20. 21. 4 5 3 5 3 5 2 5 4 3 -3 2 0 1-30 2 -1 1 5 4 0 1 4 1 1 2 5) 1 1 5 ' 4 2 1 -4 5 0 S 1 -2 _ 1 ~~ 20 2 1 0 1 0 7 10 0 1 -2 -1 0 1 -2 -1 2 2-20 0 1 -3 0 1 -3 1 20 (_l)2+4 . 0 7 1 2 2-2 a) j ~~ 20 2- 0 7 1 1 1 -1 = iV(! + 21) -2 -3 0 4 1 2 0 -1 -1 -1 3 0 -2 1 1 = -720 -1 3 4 4 -3 0 -3 4 2 -1 0 3 4 0 0 -2 4 4 2 -2 -3 2 -3 3 3 = 312 3 4 2 -1 3 0 -3 -3 -2 0 5 0 - -2 2 1 2 0 4 - -1 5 4 3 - -2 1 4 = -12 3 - -3 3 0 4 4 1 3 0 3 b) 22. 3 3 4 2 -2 382 23. 2 O 1 -4 -58 24. -3 1 1 1 3 2 2 2 20 25. 4 -1 2 1 -1 0 5 0 -90 26. 0 1 -3 0 2 0 -1 3 18 27. 2 1 -1 2 2 2 -2 2 2 3 3 0 2 3 0 0 -3 0 1 2 0 3 -12 2 302 28. 0 1 2 3 3 0 1 1 -2 0 59