Question

ajuda em matemática.........​

Answer 1

1)

$\sf\left[\begin{array}{ccc} \sf1& \sf1& \sf2\\ \sf2& \sf1& \sf3\\ \sf1& \sf4& \sf 2\end{array}\right] \sf\left |\begin{array}{ccc} \sf1& \sf1\\\sf2& \sf1\\\sf1& \sf4\end{array}\right| \\\\\ \sf det = 1 \times 1 \times 2 + 1 \times 3 \times 1 + 2 \times 2 \times 4 - (1 \times1 \times 2 + 4 \times 3 \times 1 + 2 \times 2 \times 1) \\ \sf det = 2 + 3 + 16 - (2 + 12 + 4) \\ \sf det = 2 + 3 + 16 -18 \\ \sf det = 21 - 18 \\ \sf det = 3$

2)

$\sf\left[\begin{array}{ccc} \sf3& \sf - 1& \sf - 2\\ \sf2& \sf1& \sf1\\ \sf2& \sf1& \sf - 2\end{array}\right] \sf\left |\begin{array}{ccc} \sf3& \sf - 1\\\sf2& \sf1\\\sf2& \sf1\end{array}\right| \\\\\ \sf det = 3 \times 1 \times ( - 2) + ( - 1) \times 1 \times 2 + ( - 2) \times 2 \times 1 - (2 \times 1 \times ( - 2) + 1 \times 1 \times 3 + ( - 2) \times 2 \times ( - 1)) \\ \sf det = - 6 - 2 - 4 - ( - 2 \times 1 \times 2 + 3 + 2 \times 2 \times 1) \\ \sf det = - 6 - 2 - 4 - 3 \\ \sf det = - 15$

3)

$\sf\left[\begin{array}{ccc} \sf - 3& \sf - 2& \sf - 2\\ \sf - 2& \sf - 2& \sf1\\ \sf1& \sf2& \sf 2\end{array}\right] \sf\left |\begin{array}{ccc} \sf - 3& \sf - 2\\\sf - 2& \sf - 2\\\sf1& \sf2\end{array}\right| \\\\\ \sf det = ( - 3) \times ( - 2) \times 2 + ( - 2) \times 1 \times 1 + ( - 2) \times ( - 2) \times 2 - (1 \times ( - 2) \times ( - 2) + 2 \times 1 \times ( - 3) + 2 \times ( - 2) \times ( - 2)) \\ \sf det = 12 - 2 + 8 - (4 - 6 + 8) \\ \sf det = 12 - 2 + 8 -6 \\ \sf det = 20 - 2 - 6 \\ \sf det = 20 - 8 \\ \sf det = 12$

4)

$\sf A + B = \sf\left[\begin{array}{ccc} \sf1& \sf2& \sf3\\ \sf - 4& \sf5& \sf6\\ \sf4& \sf6& \sf 8\end{array}\right] + \sf\left[\begin{array}{ccc} \sf - 7& \sf - 8& \sf9\\ \sf 12& \sf6& \sf5\\ \sf8& \sf7& \sf 4\end{array}\right] \\ \\ \sf A + B = \sf\left[\begin{array}{ccc} \sf1 + ( - 7)& \sf2 + ( - 8)& \sf3 + 9\\ \sf - 4 + 12& \sf5 + 6& \sf6 + 5\\ \sf4 + 8& \sf6 + 7& \sf 8 + 4\end{array}\right] \\ \\ \sf A + B = \sf\left[\begin{array}{ccc} \sf - 6& \sf - 6& \sf12\\ \sf8& \sf11& \sf11\\ \sf12& \sf13& \sf 12\end{array}\right] \\ \\ \\\sf A + B - C= \sf\left[\begin{array}{ccc} \sf - 6& \sf - 6& \sf12\\ \sf8& \sf11& \sf11\\ \sf12& \sf13& \sf 12\end{array}\right] - \sf\left[\begin{array}{ccc} \sf 2& \sf 3& \sf - 4\\ \sf6& \sf7& \sf1\\ \sf2& \sf8& \sf 7\end{array}\right] \\ \\ \sf A + B - C= \sf\left[\begin{array}{ccc} \sf - 6 - 2& \sf - 6 - 3& \sf12 - ( - 4)\\ \sf8 - 6& \sf11 - 7& \sf11 - 1\\ \sf12 - 2& \sf13 - 8& \sf 12 - 7\end{array}\right] \\ \\ \sf A + B - C= \sf\left[\begin{array}{ccc} \sf - 8& \sf - 9& \sf16\\ \sf2& \sf4& \sf10\\ \sf10& \sf5& \sf 5\end{array}\right]$