Atividade 2

1- P(x) = det A A = | 1 -1 1 | | 3 0 x | | 0 2 2/3 | det A = | 1 -1 1 | 3 0 x 0 2 2/3 det A = (1 ⋅ 0 ⋅ 2/3) + (-1 ⋅ x ⋅ 0) + (1 ⋅ 3 ⋅ 2) - (1 ⋅ 0 ⋅ x) - (-1 ⋅ 3 ⋅ 2/3) - (1 ⋅ 0 ⋅ 0) = (1 - x) (2) + (-1 ⋅ 3 ⋅ 2/3) = 6 + 2x + 2 = 2x + 8 = P(x) A- P(x) = 2x + 8 P(7) = 2(7) + 8 P(7) = 22 kg B- P(x) = 2x + 8 30 = 2x + 8 2x = 22 x = 11 anos 2- A = | 1 2 | | 2 3 | B = | 0 3 | | 1 4 | C = | -1 0 | | 2 -1 | I. X = A + B - C | 1 2 | + | 0 3 | = | 1+0 2+3 | = | 1 5 | | 2 3 | | 1 4 | = | 2+1 3+4 | = | 3 7 | A+B | 1 5 | - | -1 0 | = | 1-(-1) 5-0 | = | 2 5 | | 3 7 | | 2 -1 | = | 3-2 7-(-1) | = | 4 8 | (verdadeiro) II. Y = B - A - C | 0 3 | - | 1 2 | = | 0-1 3-2 | = | -1 1 | | 1 4 | | 2 3 | = | 1-2 4-3 | = | -1 1 | (verdadeiro) III. 2A - C = Z | 2 2 | = | 2 4 | | 2 2 | | 4 6 | | 2 4 | - | -1 0 | = | 3 4 | | 4 6 | | 2 -1 | = | 6 7 | (verdadeiro) Alternativa correta: b) todas as afirmações são verdadeiras. 3- camisas 3 1 3 meses botões 6 5 5 x camisas 100 50 50 100 50 50 [ 3 1 3 ] [ 100 50 ] | 50 | | 50 | [ 6 5 5 ] [ 50 50 ] | 100 | | 50 | |300 + 50 + 150 | 150 + 100 + 150 | |600 + 250 + 250 300 + 500 + 250 | |500 400| |1100 1050| 4A- a = | 1 3 | | 2 2 | 2 x 2 det a = | 1 3 | | 2 2 | det a = 1 ⋅ 2 - (2 ⋅ 3) = -4 b = | 1 3 1 | | 2 2 1 | | 1 1 3 | 3 x 3 det b = | 1 3 1 | | 2 2 1 | | 1 1 3 | det b = (1 ⋅ 2 ⋅ 3) + (3 ⋅ 1 ⋅ 1) + (1 ⋅ 2 ⋅ 1) - (1 ⋅ 2 ⋅ 1) + (1 ⋅ 2 ⋅ 2) + (1 ⋅ 3 ⋅ 3)) = 6 + 3 + 2 - (2 + 1 + 18) = -10 a² - 2b (-4)² - 2(-10) 16 + 20 = 36 S = { 36 } 4B- det | 2 x x | | -1 -2 -1 | | 3 2 x | det = (2(-2)2) + (x(-1)3) + (x(-1)x) - ((x-2)(3) + (2(-1)(-1)) + (x(-1)(2))) = -8 - 3x - x - (6x - 2 - 2x) -8 - 4x + 8x + 2 | 4x - 6 |= 8 - log4 14x - 6 = 8 - 2 14x - 6 = 6 4x - 6 = 6 4x = 6 + 6 4x = 6 + 6 x = 0/4 = 0 S= { 3 ou 0 } 5.- \{ x-2y+z=3 \ 2x+y+z=1 \ 3x-y+2z=2 \} \{ x-2y+z=3 \ 2x+y+z=1 \ x-2y+z=3 \ 3x-y+2z=2 \} x-2y+z=3 x=2y-z+3 2x+y+z=1 2(2y-z+3)+y+z=1 4y-2z+6+y+z=1 5y-z=-5 3x-y+2z=2 3(2y-z+3)-y+2z=2 6y-3z+9-y+2z=2 5y-z=-7 \{ 5y-z=-5 \ 5y-z=-7 \} 5y-z=-7 5y-(7+5y)=-5 -z=-7-5y 5y-7-5y=-5 z=7+5y 0y=2 \emptyset 5=\{(x,y,z) \in \emptyset \} 6.- \{ x+2y+z=8 \ 2x-y+z=3 \ 3x+y-z=2 \} det=\begin{vmatrix} 1 & 2 & 1 \ 2 & -1 & 1 \ 3 & 1 & -1 \end{vmatrix} det=(1(-1)(-1))+((2)(-3))+((1)(2))-((1(-1)(3))+((1)(3)(-1))+ (2(2)(-1)))=4+6+2-(-3+1-4)=15 det x=\begin{vmatrix} 8 & 2 & 1 \ 3 & -1 & 3 \ 2 & 1 & -1 \end{vmatrix} det x=(8(-1)(-1))+((2)(-3))+((1)(2))-((1)(-1)(3))+ (8(-1))+((2-3)(-1)))=8+4+3-(-2+8-6)=15 det y=\begin{vmatrix} 1 & 8 & 1 \ 2 & 3 & 1 \ 3 & -1 & -1 \end{vmatrix} det y=(1(3)(-1))+((8.2))+((1)(2))-((1)(3.3))+((1)(2))+ (8.2(-1)))=-3+24+4- (9+2-16)=30 det z=\begin{vmatrix} 1 & 2 & 8 \ 2 & -1 & 3 \ 3 & 1 & 2 \end{vmatrix} det z=(1(-1)(2))+((2-3.3))+((8.2.1))-((8(-1)(3))+((1-3.1))+((2.2.2)))=-2+18+16-(24+3+8)=45 x=\frac{15}{15}=1 \ y=\frac{30}{15}=2 \ z=\frac{45}{15}=3 S=\{ 1, 2, 3 \}