MATEMATICA

Página 3

1.1) a) 2x -3y +z = 9

x +2y -2z =-5

3x –y +3z = 8

D = 2 -3 1 2 -3

1 2 -2 1 2

3 -1 3 3 -1

D = (12 + 18 -1) – (6 +4 +9)

D = 29 -1

D = 28

Dx = 9 -3 1 9 -3

-5 2 -2 -5 2

8 -1 3 8 -1

Dx = (54 + 48 +5) – (16 + 18 +45)

Dx = 107 – 79

Dx = 28

Dy = 2 9 1 2 9

1 -5 -2 1 -5

3 8 3 3 8

Dy = (-30 -54 +8) – (-15 -32 +27)

Dy = -76 – (-20)

Dy = -56

Dz = 2 -3 9 2 -3

1 2 -5 1 2

3 -1 8 3 -1

Dz = (32 +45 -9) – (54 +10 -24)

Dz = 68 -40

Dz = 28

X = Dx = 28 = 1 Z = Dz = 28 = 1

D 28 D 28

Y = Dy = -56 = -2 S = { 1, -2, 1 }

D 28

d) x +y +z = 3

2x +2y +z = 7

3x +3y +2z = 10

3x = 10 -3y -2z

X = 10 -3y -2z

3

10 -3y -2z +3y +3z = 9

3

10 -3y -2z +3y +3z -9 = 0

Z = -1

x +y +z = 3

x +y -1 -3 = 0

x +y -4 = 0

x = 4 –y

2x +2y +z = 7

2(4 –y) +2y -1 -7 = 0

8 -2y +2y -8 = 0

0 = 0

X = 10 -3y -2z

3

4 –y = 10 -3y -2 (-1)

3

12 -12y = 10 -3y +2

-12y +3y = 2 +10 -12

-9y = 0

Y = 0

x = 4 –y

x = 4 –0

x = 4

S = { 4, 0, -1}

Página 4

2.1) Encaminharei depois, até domingo.

2.2) a) 5x -3y = 5

2x +7y = 43

D = 5 -3 = (5 x 7) – (2 x -3)

2 7 35 – (-6)

35 +6 = 41

Dx = 5 -3 = 35 – (-129)

43 7 35 + 129

Dx = 64

Dy = 5 5 = (5 x 43) – (2 x 5)

2 43 215 -10

Dy = 205

X = Dx = 164