Autor: Rochedão | Publicado: 2013-05-27T20:21:00-07:00



LISTA: &nbsp;CORPUS CHRISTI - SEGUNDOS ANOS


1)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Dê a matriz A = (aij)3x3&nbsp;em que aij = (3i - 4j) + 2



2)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Determine x, y e z que satisfaçam:
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&nbsp;x + y + 2z = 6



&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2x – 2z = -2

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;x&nbsp;+ y = 2

&nbsp; &nbsp; &nbsp; &nbsp; x&nbsp;– y = 0





3)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Resolva:&nbsp;&nbsp;A 3x3 aij = 2i - j&nbsp;&nbsp;&nbsp;B = 3x3, bij = -i-j. Faça: A + B, A- B e B -
A





&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;4) Determine a inversa
da matriz T=&nbsp;2x2, tij = 2j - i&nbsp;

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5) Se At&nbsp;é uma matriz 2x2 onde os elementos da 1a linha são 1 e 3 nessa ordem e os elementos da segunda linha são 3 e 4 nessa ordem, determine a
inversa da matriz A





&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6)
Determine&nbsp;&nbsp;At&nbsp;+ Bt +&nbsp;Ct ,
dados: 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A= 2x3, aij = j-3&nbsp;&nbsp; &nbsp; &nbsp;B= 2x3, bij = 2.(i + j) &nbsp;&nbsp; e C= 2x3, cij = 2j - i&nbsp;

&nbsp;&nbsp;&nbsp;&nbsp;7) Sejam A&nbsp;e B acima,&nbsp;&nbsp;Calcule:

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a) A –
B&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;b) A + 2B&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;c) 2A - 2B

&nbsp;&nbsp;8) Obtenha três soluções para a seguinte equação
linear x- 3y = -2


&nbsp;9) Dada a equação linear x + 2y + 4z = 1 verifique se
as triplas ordenadas abaixo são soluções.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a) (-1, 3,
-1)&nbsp;&nbsp;&nbsp;b) (1,1,1)&nbsp;&nbsp;&nbsp;c) (0,-4,-1)&nbsp;&nbsp;&nbsp;d
(0,0,1/4)


10) Numa placa, uma cantina anuncia: “ 3 sucos + 2
sanduiches&nbsp;&nbsp;= R$ 14,00 ou 2 sucos + 1 sanduiche = R$ 8,00.&nbsp;Nesse
caso, qual o preço do suco e qual o preço do sanduiche?




&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;11) Resolva
os sistemas 



&nbsp; &nbsp;a)&nbsp;&nbsp;&nbsp;<!--[endif]-->&nbsp;&nbsp;x + &nbsp;y&nbsp; = 20

&nbsp; &nbsp; &nbsp; &nbsp; 2x +3y = 55&nbsp;&nbsp;&nbsp;&nbsp; 

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;b)&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;–x &nbsp;- 2y =
- 11



&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 5x + 6y = &nbsp;&nbsp;39

&nbsp; &nbsp; c)&nbsp;&nbsp;&nbsp;<!--[endif]-->4x &nbsp;+ 6 y
= 50

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2x +
3y&nbsp; = 25 



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;12)
Verifique se (3, -1) é solução do sistema:

<!--[if !supportLists]-->&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; a-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->5x – 6y = 9

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2x + 2y = 4



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;13)&nbsp; Determine o valor de x, y, z e w no
seguintes sistemas escalonados:

<!--[if !supportLists]-->&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;a)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->x + y + 2w + z = 7

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 2x + 2y + 2w = -2

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 3x + 3y = -6

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 6x = -6

<!--[if !supportLists]-->&nbsp; &nbsp;b)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->x = 9

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;x + y + z = 16

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y+
x = 12


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 14- Prove que
os sistemas a) e &nbsp;b) &nbsp;abaixo tem a mesma solução.

&nbsp; &nbsp; &nbsp; a) &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;<!--[endif]-->x + y = 6

&nbsp; &nbsp; &nbsp; &nbsp;3x – 4y = -10 

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;b)&nbsp; &nbsp;&nbsp;<!--[endif]-->2x + 2y = 12

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 6x – 8y = - 20
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

&nbsp;&nbsp; 15) Resolva: 2x( x
+ 2y + 3z + 4y + 3) sendo x o dobro de y, z = 2, o que equivale a metade de y



&nbsp;&nbsp; 16) Multiplique: A 3x3
aij = i – 2j por B 3x3, bij = 2j - i



&nbsp;&nbsp; 17) Escreva a
matriz A = (aij)3x2 tal que aij&nbsp;= 3i – 2j + 4 e a matriz
At



&nbsp;&nbsp; 18) Faça a soma dos
elementos da diagonal principal com os elementos da diagonal secundária da
matriz &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A do exercício 16



&nbsp;&nbsp; 19) Qual o
resultado da soma da matriz identidade de ordem 3 com a matriz B do exercício 16



&nbsp;&nbsp; 20)&nbsp;&nbsp;Determine
a solução do sistema: &nbsp;&nbsp;&nbsp;&nbsp;x + y – z = 4

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;x – y – z =0

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;x + y + z = 6