Question

Alguém pfvr:--'
1-Dadas as matrizes a seguir, calcule o seu determinante: a) A = [[5, 2], [6, 7]]
b) B = [[- 2, 8], [- 3, 7]]
c) M = [[0, 1, 6], [4, - 5, 5], [3, 2, - 3]]​

Answer 1

Resposta:

A. 23 B. 10 C. 155

Explicação passo a passo:

A. multiplica cruzado e faz diferença: 5x7-12=43

B. multiplica cruzado e faz a diferença: -14-(-24)=-14+24=10

C. multiplica cruzado usando a regra de Sarrus:

(0x-5x-3+1x5x3+6x4x2)-(6x-5x3+0x5x2=1x4x-3)=

102+62=165

Answer 2

$\large\boxed{\begin{array}{l}\rm a)~\underline{\sf determinante\, matriz\,2x2:}\\\sf A=\left[\begin{array}{cc}\sf 5&\sf2\\\sf6&\sf7\end{array}\right]\\\\\sf det\,A=\left|\begin{array}{cc}\sf5&\sf2\\\sf 6&\sf7\end{array}\right|\\\\\sf det\,A=[5\cdot7]-[2\cdot6]\\\sf det\,A=[35]-[12]\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf det\,A=23}}}}\end{array}}$

$\large\boxed{\begin{array}{l}\rm b)~\underline{\sf determinante\, matriz\,2x2:}\\\sf B=\left(\begin{array}{cc}\sf-2&\sf8\\\sf-3&\sf7\end{array}\right)\\\\\sf det\,B=\left|\begin{array}{cc}\sf-2&\sf8\\\sf-3&\sf7\end{array}\right|\\\\\sf det\,B=[-2\cdot7]-[-3\cdot8]\\\sf det\,B=[-14]-[-24]\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf det\,B=10}}}}\end{array}}$

$\large\boxed{\begin{array}{l}\rm c)~\underline{\sf determinante\, matriz\,3x3:}\\\sf M=\left(\begin{array}{ccc}\sf 0&\sf1&\sf6\\\sf4&\sf-5&\sf5\\\sf3&\sf2&\sf-3\end{array}\right)\\\\\sf det\,M=\left|\begin{array}{ccc}\sf0&\sf1&\sf6\\\sf4&\sf-5&\sf5\\\sf3&\sf2&\sf-3\end{array}\right|\left|\begin{array}{cc}\sf0&\sf1\\\sf4&\sf-5\\\sf3&\sf2\end{array}\right|\\\\\sf det\,M= [0+15+48]-[-12+0+(-90)]\\\sf det\,M=[15+48]-[-12+(-90)]\\\sf det\,M=[63]-[-102]\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf det\,M=165}}}} \end{array}}$