Lista1_Matrizes_DavidSarago

Prévia do material em texto

<p>/ 1a) (aij) = 4 9 azz 9 16 = bis 2 b12 b23 3 = d C12 C13 -8 C23 13 C31 C32 C33 8 13 A 10 2) aij = (2 2 A = / 2 3 4 4 5 6 a 0 = h</p><p>A 4)a) Asxu b) as2 = 9 Temos 3x4 sao 12 j 6x6 36 ; pora quotre elementos temos, S = doze { 4x3, 1x a-1 3 2 3 b - 2 4 1 4 8- 2 a) A = aii A= 8 S S b) B= 1 bij = B= 3/2 2 5/2 B+ 1 81 2</p><p>B= 3-9 2c 2+d 24 b 3 2 2c 2+d A = 3 b=2 8 2+d = 4 A-d 9) M= b 2-Y a 0 2 3z -b b 1 2 1 3 -a C a 3z Ox -2 - => b=1 5 = => => a = -2 3z = - 3z =0 E</p><p>10) log 3 5 64 14 1 4 3 b) 2 OM -4 M 0 2x x-y 1 => - 9 i aij = 1 32; 5 6 S 4 10</p><p>-3 -2 -4 =7 3 2 4 7 3 3 t 3 8 15 8 8 = 3 15 X 14 3 14 E - 32 0 18 a) 31A-B) + + -10 13 11 E -3 3 17 6 3 45 30 39 33 -9 3 9 S1 to 0 = 0)</p><p>- 2. - 14 3 3 3 -16 0 18 4 14 + 6 ( 45 30 -45 -42 48 O -54 4 -3 0 8 8 + 1 X1 (X-A) - X3 X4 X3 - 3428 X3 X2-3 ( X4-9 6 4 X3 ) 112 100 3x4-374 4x3 4x4 140 = 112 3x2-1 = 4x2+ 100 => 3x3+6 = 4x3 X3 $ 6 = 4x4 + 140</p><p>1 2 3 - 2A A 1 2 1 1 2x - 3A = 1 2x a + 3A 2 2 2x = 3A - A 16) 2A - = B+ 1 2A 2A - of S A= (2 i B= ( 2 ) 1 12 2 1 = 2 18 2 S 18 1 4) 4/5 1815</p><p>1 1 2 2 = A+B (A+B) = S 24 A 26 b) 2 12 24 25 24 = 12 24 S 12 24 - X e' a A 1 2 3 0 X 4-5-7 -1 3</p><p>/ A 10 1 2 Ad A.B = 1 / = ( Ad 1 20) A = B ( 1 -4 - 2 ( 24 = x2 4x4 8x2 = 2 - 4x1 + = E + = 3 X = 1/2</p><p>A = 4 -2 20 a) AB : 2) -2 4 8 BA : 20 4 8 4 -4 ) -2 4 8 A = 4 4 -2 8-8 -4+4 20 S 12 14 3 13 B.A 16 7 3 11 =</p><p>23. A = 2 +4A-SIz 2 1 2 4A 4 = ( Resultodo = 9 8 24. A 2 3 9 1 3 $ 4 2 2 20 A1 2 0 4 2 6 8 4 2 4 A 2.3 3 2 3 2. 3 4 2 1 2 / 0 2 0 14 20 8 20 29 11 8 11 5</p><p>c) 25) det 0 matriz 10 det A 10 7 6 6/10 -2/40 4/10 6-7 = adj 6-2 b) 12 det A = - det A 10 ( 0 01 -12 1 - + 8 d) = 2 1+ 0 det = 1 3 2 + A.A (d - adj A = 1 -2 1 = 0 0 1 -2 = 0 0 1 1 -2 9</p><p>/ / 27) det B 1-b2 1 A-1 = = 0 0 b b=0 28) A= ( B= 210 S ( 3 5 12 1 20 = 4 02</p><p>= + A AB BA + sea 30) 3 5 0 3 -9 i 022 7 10 1 1 4 1 det A= 2.13 + adj A = 13-1-3 13-4-9 -4 80-1 13/25 -4/25 1/25 -1 2 6 A -03 6 -1/25 8/25 2/25 -3/25 6/25 B- det B = adj(B) = -2 2/01 2 2 85 2 -2 9 2 A 4/6 10 2/6 2/3 -1/3 2/6 = 1/3 -1/3 1/6 1/3</p><p>/ det C = adj ( = 10/-5 -7/-5 b) - 110 2/3 -1/3 1/3 1/3 1/3 -1/3 1/3 -1/3+1/3 1/3 0 0 1 0 1/2 1 c) = + = = 3B.A + 3I 110 13/25 -4/25 B.A 8/25 2/25 102 -3/25 -1/25 6/25 12/25 4/25 1/25 36/25 12/25 3/25 300 = -8/25 14/25 16/25 3 -24/25 48/25 + 0 3 0 7/25 -6/25 11/25 21/25 33/25 0 03 111 12/25 3/25 25 24/25 117/25 48/25 21/25 -18/25 108/25</p>