Question

O sistema abaixo nas variáveis x e y,

{ ax + 2y = 1
{ 3ax + ay = 2’

A) admite a solução (0, 0), se a = 0
B) é homogêneo
C) é indeterminado se a ≠ 1
D) é impossível se a = 6
E) é indeterminado se a = 2

Help!!

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm Express\tilde ao\,matricial\,de\,um\,sistema\,linear}\\\begin{cases}\sf a_{11}x+a_{12}y=c_1\\\sf a_{21}x+a_{22}y=c_2\end{cases}\implies\begin{bmatrix}\sf a_{11}&\sf a_{12}\\\sf a_{21}&\sf a_{22}\end{bmatrix}\cdot\begin{bmatrix}\sf x\\\sf y\end{bmatrix}=\begin{bmatrix}\sf c_1\\\sf c_2\end{bmatrix}\end{array}}$

$\Large\boxed{\begin{array}{l}\bf" A\,matriz\,quadrada\,dos\,coeficientes\\\bf multiplicada\,pela\,matriz\,coluna\\\bf das\,vari\acute aveis\\\bf resulta\,na\,matriz\,coluna\\\bf dos\,termos\,independentes"\end{array}}$

$\large\boxed{\begin{array}{l}\begin{cases}\sf ax+2y=1\\\sf3ax+ay=2\end{cases}\implies\begin{bmatrix}\sf a&\sf 2\\\sf 3a&\sf a\end{bmatrix}\cdot\begin{bmatrix} \sf x\\\sf y\end{bmatrix}=\begin{bmatrix}\sf 1\\\sf 2\end{bmatrix}\end{array}}$

$\large\boxed{\begin{array}{l}\sf A=\begin{bmatrix}\sf a&\sf 2\\\sf 3a&\sf a\end{bmatrix}\\\sf det\,A=a^2-6a\\\sf para\,ter\,soluc_{\!\!,}\tilde ao\,precisamos\,garantir\,que\\\sf det\,A\ne0\\\sf logo\\\sf a^2-6a\ne0\\\sf a\cdot(a-6)\ne0\\\sf a\ne0~e~a-6\ne0\\\sf a\ne6\\\sf portanto\,se\,a\ne0\,e\,a\ne6\,o\,sistema\,\acute e\, SPD\end{array}}$

$\large\boxed{\begin{array}{l}\sf se~a=6~o\,sistema\,\acute e\,imposs\acute ivel.\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese\,alternativa\,D}}}}\end{array}}$