Question

Qual o determinante da matriz
abaixo?
1 4 0
0 3 2
2 1 2 ​

Answer 1

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⠀⠀☞ A determinante desta matriz é igual a 20. ✅

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⠀⠀ O método mais comum para encontrarmos a determinante de uma matriz 3x3 é através do Método de Sarrus, onde copiamos as duas primeiras colunas após a terceira coluna e subtraímos a soma das três diagonais iniciadas em $\sf a_{11}$ pela soma das três diagonais iniciadas em $\sf a_{15}$.

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$\sf\LARGE\blue{\left[\begin{array}{ccc|cc}1&4&0&1&4\\0&3&2&0&3\\2&1&2&2&1\\\end{array}\right]}$

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$\LARGE\sf\blue{\left[\begin{array}{ccc|cc}1&.&.&.&.\\.&3&.&.&.\\.&.&2&.&.\\\end{array}\right]}$

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$\blue{\sf Det(M) = 1 \cdot 3 \cdot 2 + }$  

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$\LARGE\sf\blue{\left[\begin{array}{ccc|cc}.&4&.&.&.\\.&.&2&.&.\\.&.&.&2&.\\\end{array}\right]}$

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$\blue{\sf Det(M) = 1 \cdot 3 \cdot 2 + 4 \cdot 2 \cdot 2 + }$  

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$\LARGE\sf\blue{\left[\begin{array}{ccc|cc}.&.&0&.&.\\.&.&.&0&.\\.&.&.&.&1\\\end{array}\right]}$

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$\blue{\sf Det(M) = 1 \cdot 3 \cdot 2 + 4 \cdot 2 \cdot 2 + 0 \cdot 0 \cdot 1 - }$  

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$\LARGE\sf\blue{\left[\begin{array}{ccc|cc}.&.&.&.&4\\.&.&.&0&.\\.&.&2&.&.\\\end{array}\right]}$

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$\blue{\sf Det(M) = 1 \cdot 3 \cdot 2 + 4 \cdot 2 \cdot 2 + 0 \cdot 0 \cdot 1 - 4 \cdot 0 \cdot 2}$  

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$\LARGE\sf\blue{\left[\begin{array}{ccc|cc}.&.&.&1&.\\.&.&2&.&.\\.&1&.&.&.\\\end{array}\right]}$

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$\blue{\sf Det(M) = 1 \cdot 3 \cdot 2 + 4 \cdot 2 \cdot 2 + 0 \cdot 0 \cdot 1 - 4 \cdot 0 \cdot 2 - 1 \cdot 2 \cdot 1 - }$  

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$\LARGE\sf\blue{\left[\begin{array}{ccc|cc}.&.&0&.&.\\.&3&.&.&.\\2&.&.&.&.\\\end{array}\right]}$  

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$\blue{\sf Det(M) = 1 \cdot 3 \cdot 2 + 4 \cdot 2 \cdot 2 + 0 \cdot 0 \cdot 1 - 4 \cdot 0 \cdot 2 - 1 \cdot 2 \cdot 1 - 0 \cdot 3 \cdot 2}$

$\Large\blue{\sf Det(M) = 6 + 16 + 0 - 0 - 0 - 2}$

$\Large\blue{\sf Det(M) = 20}$

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$\huge\green{\boxed{\rm~~~\blue{Det(M) = 20~~~}}}$ ✅

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$\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

⠀⠀☀️ Exercício semelhante:

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⠀⠀✈https://brainly.com.br/tarefa/38167067

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Answer 2

Resposta:

1     4     0

0    3     2

2     1     2 ​

L3=L3-2L1

1       4       0

0      3       2

0     -7      2 ​

det=(-1)¹⁺¹ * 1 * det A

A=

3   2

-7   2

det=3*2-(-7*2) =6+14=20

det=(-1)¹⁺¹ * 1 * 20   = 20