Considere as matrizes abaixo:
M1=[39]. M2= [2 3 x]
[2x]. [2-2 0]
[-1 2 1]
O valor de x para ser M1=det M2 é:
a)2 b)4 c)8 d)10 é)12
Crazysong:
Na escrita ficou meio bagunçada,mas a M1 é 2x2 e a Menina é 3x3 ! A M1 é 39
M1 =39/2x. M2= 23x/2-20/-121
Soluções para a tarefa
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A matriz 
e 
:
A questão afirma que o
. Calculando o determinante das matrizes teremos:
๏ Determinante M1:
![\mathsf{det(M1)=\left[\begin{array}{cc}3&9\\2&x\end{array}\right]}\\\\\\\mathsf{det\left(M1\right)=\left(3\cdot x\right)-\left(9\cdot 2\right)}\\\\\mathsf{det\left(M1\right)=3x-18}](https://tex.z-dn.net/?f=%5Cmathsf%7Bdet%28M1%29%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%26amp%3B9%5C%5C2%26amp%3Bx%5Cend%7Barray%7D%5Cright%5D%7D%5C%5C%5C%5C%5C%5C%5Cmathsf%7Bdet%5Cleft%28M1%5Cright%29%3D%5Cleft%283%5Ccdot+x%5Cright%29-%5Cleft%289%5Ccdot+2%5Cright%29%7D%5C%5C%5C%5C%5Cmathsf%7Bdet%5Cleft%28M1%5Cright%29%3D3x-18%7D "\mathsf{det(M1)=\left[\begin{array}{cc}3&9\\2&x\end{array}\right]}\\\\\\\mathsf{det\left(M1\right)=\left(3\cdot x\right)-\left(9\cdot 2\right)}\\\\\mathsf{det\left(M1\right)=3x-18}")
๏ Determinante M2: Por se tratar de uma matriz 3x3 irei utilizar a Regra de Sarrus:
![\mathsf{det(M2)=\left[\begin{array}{cccccc}2&3&x&|&2&3\\2&-2&0&|&2&-2\\-1&2&1&|&-1&2\end{array}\right]}](https://tex.z-dn.net/?f=%5Cmathsf%7Bdet%28M2%29%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccccc%7D2%26amp%3B3%26amp%3Bx%26amp%3B%7C%26amp%3B2%26amp%3B3%5C%5C2%26amp%3B-2%26amp%3B0%26amp%3B%7C%26amp%3B2%26amp%3B-2%5C%5C-1%26amp%3B2%26amp%3B1%26amp%3B%7C%26amp%3B-1%26amp%3B2%5Cend%7Barray%7D%5Cright%5D%7D "\mathsf{det(M2)=\left[\begin{array}{cccccc}2&3&x&|&2&3\\2&-2&0&|&2&-2\\-1&2&1&|&-1&2\end{array}\right]}")
![\mathsf{det\left(M2\right)=\left(x\cdot 2\cdot 2\right)+\left[3\cdot \:0\cdot \:\left(-1\right)\right]+\left[2\cdot \:\left(-2\right)\cdot \:1\right]}\\\mathsf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: -\left[x\cdot \left(-2\right)\cdot \left(-1\right)\right]-\left(2\cdot 0\cdot 2\right)-\left(3\cdot 2\cdot 1\right)}\\\\\mathsf{det\left(M2\right)=4x-4-2x-6}\\\\\mathsf{det\left(M2\right)=2x-10}](https://tex.z-dn.net/?f=%5Cmathsf%7Bdet%5Cleft%28M2%5Cright%29%3D%5Cleft%28x%5Ccdot+2%5Ccdot+2%5Cright%29%2B%5Cleft%5B3%5Ccdot+%5C%3A0%5Ccdot+%5C%3A%5Cleft%28-1%5Cright%29%5Cright%5D%2B%5Cleft%5B2%5Ccdot+%5C%3A%5Cleft%28-2%5Cright%29%5Ccdot+%5C%3A1%5Cright%5D%7D%5C%5C%5Cmathsf%7B%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+-%5Cleft%5Bx%5Ccdot+%5Cleft%28-2%5Cright%29%5Ccdot+%5Cleft%28-1%5Cright%29%5Cright%5D-%5Cleft%282%5Ccdot+0%5Ccdot+2%5Cright%29-%5Cleft%283%5Ccdot+2%5Ccdot+1%5Cright%29%7D%5C%5C%5C%5C%5Cmathsf%7Bdet%5Cleft%28M2%5Cright%29%3D4x-4-2x-6%7D%5C%5C%5C%5C%5Cmathsf%7Bdet%5Cleft%28M2%5Cright%29%3D2x-10%7D "\mathsf{det\left(M2\right)=\left(x\cdot 2\cdot 2\right)+\left[3\cdot \:0\cdot \:\left(-1\right)\right]+\left[2\cdot \:\left(-2\right)\cdot \:1\right]}\\\mathsf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: -\left[x\cdot \left(-2\right)\cdot \left(-1\right)\right]-\left(2\cdot 0\cdot 2\right)-\left(3\cdot 2\cdot 1\right)}\\\\\mathsf{det\left(M2\right)=4x-4-2x-6}\\\\\mathsf{det\left(M2\right)=2x-10}")
Igualando os 2 determinantes:
A questão afirma que o
๏ Determinante M1:
๏ Determinante M2: Por se tratar de uma matriz 3x3 irei utilizar a Regra de Sarrus:
Igualando os 2 determinantes:
Entendi muito obg !!
Por nada =D
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