Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\begin{bmatrix}\cancel3&\cancel-2&\cancel1\\\cancel-1&\cancel0&\cancel1\\\cancel4&\cancel\textsf{k}&\cancel1\end{bmatrix}[/tex]
[tex]\mathsf{D = ( 0 - 8 - k) - ( 0 + 3k + 2)}[/tex]
[tex]\mathsf{D = -4k - 10}[/tex]
[tex]\mathsf{A = \dfrac{|\:D\:|}{2}}[/tex]
[tex]\mathsf{13 = \dfrac{|\:-4k -10\:|}{2}}[/tex]
[tex]\mathsf{|\:-4k -10\:| = 26}[/tex]
[tex]\mathsf{-4k -10\ = -26}[/tex]
[tex]\mathsf{4k = 26 - 10}[/tex]
[tex]\mathsf{4k = 16}[/tex]
[tex]\boxed{\boxed{\mathsf{k = 4}}}[/tex]
[tex]\boxed{\boxed{\mathsf{R(4;4)}}}[/tex]
