Matriz

i = número da linha

j = número da coluna

A 3 , 4 onde ai,j = i +2j - 3

3 > i > 1 e 4 > j > 1

Matriz

A= A 11 A 12 A 13 A 14 A= 0 2 4 6

A 21 A 22 A 23 A 24 => 1 3 5 7

A 31 A 32 A 33 A 34 2 4 6 8

1 + 2 x 1 - 3 = 0 1 + 2 x 2 - 3 = 2 1 + 2 x 3 - 3 = 4 1 + 2 x 4 - 3 = 6

2 + 2 x 1 - 3 = 1 2 + 2 x 2 - 3 = 3 2 + 2 x 3 - 3 = 5 2 + 2 x 4 - 3 = 7

3 + 2 x 1 - 3 = 2 3 + 2 x 2 - 3 = 4 3 + 2 x 3 - 3 = 6 3 + 2 x 4 - 3 = 8

B 3 , 4 onde bi,j = -2i +3j-6

3 > i > 1 e 4 > j > 1

Matriz

B= B 11 B 12 B 13 B 14 B= -5 -2 1 4

B 21 B 22 B 23 B 24 => -7 -4 -1 2

B 31 B 32 B 33 B 34 -9 -6 -3 0

-2 x 1 + 3 x 1 - 6 = -5 -2 x 1 + 3 x 2 - 6 = -2 -2 x 1 + 3 x 3 - 6 = 1 -2 x 1 + 3 x 4 - 6 = 4

-2 x 2 + 3 x 1 - 6 = -7 -2 x 2 + 3 x 2 - 6 = -4 -2 x 2 + 3 x 3 - 6 = -1 -2 x 2 + 3 x 4 - 6 = 2

-2 x 3 + 3 x 1 - 6 = -9 -2 x 3 + 3 x 2 - 6 = -6 -2 x 3 + 3 x 3 - 6 = -3 -2 x 3 + 3 x 4 - 6 = 0

Calcule:

t

a-) A . A = C

A= 0 2 4 6 t 0 1 2 56 68 80

A 1 3 5 7 x A 2 3 4 => C = 68 84 100

2 4 6 8 4 5 6 80 100 120

6 7 8

0 x 0 + 2 x 2 + 4 x 4 + 6 x 6 = 56 0 x 1 + 2 x 3 + 4 x 5 + 6 x 7 = 68 0 x 2 + 2 x 4 + 4 x 6 + 6 x 8 = 80

1 x 0 + 3 x 2 + 5 x 4 + 7 x 6 = 68 1 x 1 + 3 x 3 + 5 x 5 + 7 x 7 = 84 1 x 2 + 3 x 4 + 5 x 6 + 7 x 8 = 100

2 x 0 + 4 x 2 + 6 x 4 + 8 x 6 = 80 2 x 1 + 4 x 3 + 6 x 5 + 8 x 7 = 100 2 x 2 + 4 x 4 + 6 x 6 + 8 x 8 = 120

t

b-) B . B = D

-5 -2 1 4 t -5 -7 -9 46 50 54

B -7 -4 -1 2 x B -2 -4 -6 => D = 50 70 90

-9 -6 -3 0 1 -1 -3 54 90 126

4 2 0

-5 x -5 + -2 x -2 + 1 x 1 + 4 x 4 = 46 -5 x -7 + -2 x -4 + 1 x -1 + 4 x 2 = 50 -5 x -9 + -2 x -6 + 1 x -3 + 4 x 0 = 54

-7 x -5 + -4 x -2 + -1 x 1 + 2 x 4 = 50 -7 x -7 + -4 x -4 + -1 x -1 + 2 x 2 = 70 -7 x -9 + -4 x -6 + -1 x -3 + 2 x 0 = 90

-9 x -5 + -6 x -2 + -3 x 1