K matici A určete matici inverzní A 1. For given matrix A find its inverse A-1. 1)A 6 -4 -17 1 0 0 |-1| 1 3 0 1 0 2 -1 -6 0 0 1 -1 1 3 0 1 0 0 2 1 1 6 0 0 m 0 0 2 1 -1 0 3 0 -1 -1 0 1 0 0 2 1 0 0 m 1 2 -2 1 0 0 3 7 -5 0 1 0 0 2 1 0 0 1 1 2 -2 A- 2) A l-ll 2 3 1 0 0 2 0 1 0 1 0 1 1 2 0 0 1 -1 2 3 1 0 0 0 4 7 2 1 0 0 Í31 5 1 0 1 -1 2 3 1 0 0 0 m 2 1 1 -1 0 3 5 1 0 1 -1 0 -1 -1 -2 2 0 1 2 1 1 -1 0 0 m 2 3 -4 1 0 0 -1 -1 2 0 1 0 -3 -5 7 0 0 1 2 3 -4 A- 3) A 3 1 2 1 0 0 0 2 1 0 1 0 |-!| 3 3 0 0 1 -1 3 3 0 0 1 0 Í21 1 0 1 0 0 10 11 1 0 3 -2 0 3 0 -3 2 0 12 6 0 6 0 0 0 Í61 1 -5 3 4 0 0 1 1 -1 0 12 0 -1 11 -3 0 0 12 2 -10 6 12 0 0 3 3 -3 0 12 0 -1 11 -3 0 0 12 2 -10 6 Í21 0 3 1 0 0 -3 3 1 0 1 0 -3 2 -2 0 0 1 2 0 3 1 0 0 0 6 11 3 2 0 0 m 5 3 0 2 2 0 3 1 0 0 0 4 5 3 0 2 0 0 m -3 4 -6 14 0 0 16 -12 18 0 -28 0 -36 20 -44 0 0 7 -3 4 -6 7 0 0 8 -6 9 0 7 0 9 -5 11 0 0 7 -3 4 -6 A- 5) A 3 -2 1 i 0 0 2 0 -1 0 1 0 m -3 3 0 0 1 i -3 3 0 0 1 0 Í61 -7 0 1 -2 0 7 -8 1 0 -3 1 -3 3 0 0 1 0 6 -7 0 1 -2 0 m -1 1 -1 -1 1 0 0 3 -3 -2 0 1 -1 1 -1 -1 0 0 E3 -6 7 4 Robert Mak, www.mendelu.cz/ marik, Typeset by A\z[S-T^)i 2 1 O O 1 o o A-1-- 6) A 1 0 4 1 0 0 m -1 1 0 1 0 i 2 6 0 0 1 i -1 1 0 1 0 0 m 3 1 -1 0 0 3 5 0 -1 1 1 0 4 1 0 0 0 1 3 1 -1 0 0 0 -4 -3 2 1 1 0 0 -2 2 1 0 4 0 -5 2 3 0 0 4 3 -1 -1 4 0 0 -8 8 4 0 4 0 -5 2 3 0 0 4 3 -1 -1 A- 7) A 2 1 1 1 0 0 1 2 2 0 1 0 |-!| 0 -1 0 0 1 1 0 1 0 0 -1 0 m -1 1 0 2 0 2 1 0 1 1 1 0 1 0 0 -1 0 1 -1 1 0 2 0 0 3 -2 1 -3 3 0 3 0 0 -3 0 3 -3 3 0 6 0 0 [31 -2 1 -3 3 0 0 2 -1 0 0 3 0 1 1 3 0 0 3 -2 1 -3 A- 8) A 2 -1 0 1 1 3 -2 L 1 0 4\ -3 L -L -1 1 2 6 J 1 0 4 1 0 0 1 -1 1 0 1 0 1 2 6 0 0 1 1 0 4 1 0 0 0 -1 -3 -1 1 0 0 2 2 -1 0 1 1 0 4 1 0 0 0 1 3 1 -1 0 0 0 -4 -3 2 1 1 0 0 -2 2 1 0 4 0 -5 2 3 0 0 4 3 -2 -1 A- 9) A 5 -1 5 1 0 0 2 0 2 0 1 0 -3 -3 1 0 0 1 5 -1 5 1 0 0 2 0 2 0 1 0 R -3 3 0 1 1 -i -3 3 0 1 1 0 -16 20 1 5 5 0 -6 8 0 3 2 -1 -3 3 0 1 1 0 Í2l -4 1 -4 -1 0 -6 8 0 3 2 2 0 6 -3 1 1 0 2 4 1 -4 -1 0 0 -4 3 -9 -1 4 0 0 3 -7 -1 0 2 0 -2 5 0 0 0 4 -3 9 1 4 0 0 3 -7 -1 0 4 0 -4 10 0 0 0 4 -3 9 1 A -i _ i 4 3 -7 -1 -4 10 0 -3 9 1 10) A m 4 3 1 0 0 i 3 3 0 1 0 2 5 3 0 0 1 1 4 3 1 0 0 0 R 0 -1 1 0 0 -3 -3 -2 0 1 3 1 0 3 -3 4 0 0 -1 0 -1 1 0 0 0 R 1 -3 1 1 0 0 -2 1 1 0 1 0 1 -1 0 0 0 -3 1 -3 1 3 0 0 -6 3 3 0 3 0 3 -3 0 0 0 3 -1 3 -1 A- 11) A -6 3 3 3 - -3 0 -1 3 -1 2 2 2 2 1 2 1 -2 1 0 1 0 2 0 0 2 2 2 2 2 1 0 0 0 1 2 1 -2 0 1 0 0 m 0 1 0 0 0 1 0 2 0 0 2 0 0 0 1 1 0 1 0 0 0 1 0 0 Í2l 0 2 1 0 -2 0 0 2 0 -2 0 1 -1 0 0 0 -2 2 0 0 -2 1 1 0 1 0 0 0 1 0 0 2 0 2 1 0 -2 0 0 0 0 -4 -1 1 1 0 0 0 R 2 0 0 -2 1 2 0 0 2 0 0 0 1 0 2 0 2 1 0 -2 0 0 0 -2 2 0 0 -2 1 0 0 0 R 1 -1 -1 0 4 0 0 0 -1 1 1 2 0 4 0 0 1 1 -3 0 0 0 4 0 1 -1 3 -2 0 0 0 4 1 -1 -1 0 A- 12) A Í2l 1 0 0 1 0 0 0 3 2 0 0 0 1 0 0 1 1 3 4 0 0 1 0 2 -1 2 3 0 0 0 1 2 1 0 0 1 0 0 0 m 1 0 0 -1 1 0 0 i 1 3 4 0 0 1 0 2 -1 2 3 0 0 0 1 1 1 0 0 -1 1 0 0 0 R 0 0 3 -2 0 0 0 0 3 4 1 -1 1 0 0 -3 2 3 2 -2 0 1 1 0 0 0 2 -1 0 0 0 -1 0 0 3 -2 0 0 0 0 3 4 1 -1 1 0 0 0 [21 3 -7 4 0 1 1 0 0 0 2 -1 0 0 0 -1 0 0 3 -2 0 0 0 0 m 1 8 -5 1 -1 0 0 2 3 -7 4 0 1 1 0 0 0 2 -1 0 0 0 1 0 0 -3 2 0 0 0 0 1 1 8 -5 1 -1 0 0 0 m -23 14 -2 3 1 0 0 0 2 -1 0 0 0 1 0 0 -3 2 0 0 0 0 1 0 31 -19 3 -4 0 0 0 1 -23 14 -2 3 A- 2 -1 0 0 -3 2 0 0 31 -19 3 -4 23 14 -2 3 13) A 3 -2 0 1 0 2 2 1 1 -2 -3 -2 0 1 2 1 3 -2 0 1 1 0 0 0 0 2 2 1 0 1 0 0 1 -2 -3 -2 0 0 1 0 0 1 2 1 0 0 0 1 1 -2 -3 -2 0 0 1 0 0 m 2 1 0 0 0 1 0 4 9 7 1 0 -3 0 0 2 2 1 0 1 0 0 1 0 1 0 0 0 1 2 0 1 2 1 0 0 0 1 0 0 m 3 1 0 -3 -4 0 0 -2 -1 0 1 0 -2 1 0 0 -3 -1 0 4 6 0 1 0 -5 -2 0 6 9 0 0 1 3 1 0 -3 -4 0 0 0 5 2 1 -6 -10 5 0 0 0 1 3 2 0 0 1 0 0 0 1 0 -1 0 0 5 0 -1 -3 3 10 0 0 0 5 2 1 -6 -10 5 O O 5 O O O O A- 0 -5 10 -10 7) A A- 8) A 1)A A- 2) A 9) A A- A- 3) A 10) A A- 4) A A- 11) A A- A- 10 7 4 5) A A- 6) A 12) A A- 13) A A- A-