Question

Resolva os determinantes

Answer 1

Resposta:

Explicação passo a passo:

A)

$\left[\begin{array}{ccc}2&6\\7&5\end{array}\right] =$

2*6 -(7*6) = 12 - 42 = - 30

B)

$\left[\begin{array}{ccc}-4&6\\-2&10\end{array}\right] =$

-4*10 - ( -2*6)= -40 -(-12)= -40 +12= -28

C)

$\left[\begin{array}{ccc}-8&-5\\-2&-3\end{array}\right] =$

-8*(-3) - ( -2*(-5))= -18 -( 15) = -18 - 15 = -33

D)

$\left[\begin{array}{ccc}x&4\\3&2\end{array}\right] =5$

x*2 - ( 4 *3) =5

2x - 12 =5

2x =12 +5

2x =17

x = $\frac{17}{2}$

E)

$\left[\begin{array}{ccc}-5&x\\-3&2\end{array}\right]= -4$

-5*2 -( x*(-3)) = -4

-10 -( -3x)= -4

-10 +3x = -4

3x = 10 -4

3x = 6

x = $\frac{6}{3}$

x= 2

F)

$\left[\begin{array}{ccc}x+1&10\\-4&3\end{array}\right] =2$

(x+1)*3 - (10* (-4))=2

3x +3 -(-40) = 2

3x+ 3 +40 =2

3x +43 =2

3x = -43 +2

3x = 41

x = $\frac{41}{3}$

G)

$\left[\begin{array}{ccc}2&4&5\\3&2&1\\0&3&4\end{array}\right] =$

$\left[\begin{array}{ccc}2&4&5\\3&2&1\\0&3&4\end{array}\right] \begin{array}{ccc}2&4\\3&2\\0&3\end{array}\right]=$

2*2*4 +4*1*0 + 5*3*3 -( 5*2*0 + 2*1*3 + 4*3*4)

16 + 0 + 45 -( 0 + 6 + 48)

61 - 54

7

H)

$\left[\begin{array}{ccc}-2&5&-1\\-3&-1&-2\\-4&1&5\end{array}\right] =$

$\left[\begin{array}{ccc}-2&5&-1\\-3&-1&-2\\-4&1&5\end{array}\right] \begin{array}{ccc}-2&5\\-3&-1\\-4&1\end{array}\right] =$

-2*(-1)*5 + 5*(-2)*(-4) + -1*(-3)*1 -( -1*(-1)*(-4) + ((-2)*(-2)*1)+ 5*(-3)*5)

10 + 40 +3 -( -4 + 4 -45)

53 - (-45)

53 +45

98