Question

Observe a matriz A e sua matriz inversa, em seguida calcule m + n. ​

Answer 1

Resposta:

Letra B

Explicação passo-a-passo:

Answer 2

Explicação passo-a-passo:

$\sf A\cdot A^{-1}=I$

$\sf \Big[\begin{array}{cc} \sf m & \sf -2 \\ \sf 1 & \sf 0 \end{array}\Big]\cdot\Big[\begin{array}{cc} \sf 0 & \sf n \\ \sf -\frac{1}{2} & \sf 3 \end{array}\Big]=\Big[\begin{array}{cc} \sf 1 & \sf 0 \\ \sf 0 & \sf 1 \end{array}\Big]$

$\sf \Big[\begin{array}{cc} \sf m\cdot0+(-2)\cdot\Big(-\frac{1}{2}\Big) & \sf m\cdot n+(-2)\cdot3 \\ \sf 1\cdot0+0\cdot\Big(-\frac{1}{2}\Big) & \sf 1\cdot n+0\cdot3 \end{array}\Big]=\Big[\begin{array}{cc} \sf 1 & \sf 0 \\ \sf 0 & \sf 1 \end{array}\Big]$

$\sf \Big[\begin{array}{cc} \sf 0+1 & \sf mn-6 \\ \sf 0+0 & \sf n+0 \end{array}\Big]=\Big[\begin{array}{cc} \sf 1 & \sf 0 \\ \sf 0 & \sf 1 \end{array}\Big]$

$\sf \Big[\begin{array}{cc} \sf 1 & \sf m\cdot n-6 \\ \sf 0 & \sf n \end{array}\Big]=\Big[\begin{array}{cc} \sf 1 & \sf 0 \\ \sf 0 & \sf 1 \end{array}\Big]$

Devemos ter:

• $\sf m\cdot n-6=0$

• $\sf \red{n=1}$

Substituindo $\sf n~por~1~em~m\cdot n-6=0$:

$\sf m\cdot n-6=0$

$\sf m\cdot1-6=0$

$\sf m-6=0$

$\sf \red{m=6}$

Logo:

$\sf m+n=6+1$

$\sf \red{m+n=7}$

Alternativa B