Question

alguém consegue me ajudar ? ​

Answer 1

Explicação passo-a-passo:

5)

a) $A=\left[\begin{array}{cc} 2&-1 \\ 1&5 \end{array}\right]$

$\text{Det}~A=2\cdot5-1\cdot(-1)$

$\text{Det}~A=10+1$

$\text{Det}~A=11$

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

$\text{Det}~A=1\cdot(-4)\cdot1+2\cdot5\cdot1+(-1)\cdot3\cdot1-1\cdot(-4)\cdot(-1)-1\cdot5\cdot1-1\cdot3\cdot2$

$\text{Det}~A=-4+10-3-4-5-6$

$\text{Det}~A=-12$

6) $\begin{cases} x-y=-3 \\ x+y=5 \end{cases}$

$D=\left(\begin{array}{cc} 1&-1 \\ 1&1 \end{array}\right)$

$\text{Det}~D=1\cdot1-(-1)\cdot1$

$\text{Det}~D=1+1$

$\text{Det}~D=2$

$D_x=\left(\begin{array}{cc} -3&-1 \\ 5&1 \end{array}\right)$

$\text{Det}~D_x=(-3)\cdot1-(-1)\cdot\cdot5$

$\text{Det}~D_x=-3+5$

$\text{Det}~D_x=2$

$D_y=\left(\begin{array}{cc} 1&-3 \\ 1&5 \end{array}\right)$

$\text{Det}~D_y=1\cdot5-(-3)\cdot1$

$\text{Det}~D_y=5+3$

$\text{Det}~D_y=8$

Desse modo:

$x=\dfrac{D_x}{D}=\dfrac{2}{2}=1$

$y=\dfrac{D_y}{D}=\dfrac{8}{2}=4$

Logo, $(x,y)=(1,4)$