#Title: Sistema de tr?s equacoes lineares caso II - Imposs?vel

#Let:

n a11 = [1 , 2 , 3 , -2 , -1 , -3 , 4] ;

n a12 = [1 , 2 , 3 , -2 , -1 , -3 , 4] ;

n a13 = [1 , 2 , 3 , -2 , -1 , -3 , 4] ;

n b1 = [1 , 2 , 3 , -2 , -1 , -3 , 4] ;

n a22p = [1 , 2 , 3 , -2 , -1 , -3 , 4] ;

n a23p = [1 , 2 , 3 , -2 , -1 , -3 , 4] ;

n b2p = [1 , 2 , 3 , -2 , -1 , -3 , 4] ;

n b3pp = [1 , 2 , 3 , -2 , -1 , -3 , 4] ;

n m21 = [1 , 2 , 3 , -2 , -1 , -3 , 4] ;

n m31 = [1 , 2 , 3 , -2 , -1 , -3 , 4] ;

n m32 = [1 , 2 , 3 , -2 , -1 , -3 , 4] ;


cn a21 = #m21 * #a11 ;

cn a22 = #a22p + #m21 * #a12 ;

cn a23 = #a23p + #m21 * #a13 ;

cn b2 = #b2p + #m21 * #b1 ;



cn a31 = #m31 * #a11 ;


cn a32p = #m32 * #a22p ;

cn a33p = #m32 * #a23p ;

cn b3p = #b3pp + #m32 * #b2p ;



cn a32 = #a32p + #m31 * #a12 ;

cn a33 = #a33p + #m31 * #a13 ;

cn b3 = #b3p + #m31 * #b1 ;



#Question:

\noindent Seja $(S)$ o sistema de equa??es lineares cuja matriz dos coeficientes
? $A=\smleft #a11 & #a12 & #a13 \\ #a21 & #a22 & #a23 \\ #a31 & #a32 & #a33 \smright$ e o vector
dos termos independentes ? $b=\smleft #b1 \\ #b2 \\ #b3 \smright$. Determine $\CS_{(S)}$.
#Suggestion:

\noindent Utilize o M?todo de Gauss.


#Solution:

\begin{align*}
\left[
\begin{array}{ccc|c}
\fbox{#a11} & #a12 & #a13 & #b1 \\
#a21 & #a22 & #a23 & #b2 \\
#a31 & #a32 & #a33 & #b3
\end{array}
\right]
&
\begin{array}{l}
\xlongleftrightarrow{\hspace{2.2cm}}\\
\ell_2\leftarrow\ell_2-(#m21)\ell_1\\
\ell_3\leftarrow\ell_3-(#m31)\ell_1\\
\end{array}
\left[
\begin{array}{ccc|c}
#a11 & #a12 & #a13 & #b1 \\
0 & \fbox{#a22p} & #a23p & #b2p \\
0 & #a32p & #a33p & #b3p
\end{array}
\right]
\\
&
\begin{array}{l}
\xlongleftrightarrow{\hspace{2.2cm}}\\
\\
\ell_3\leftarrow\ell_3-(#m32)\ell_2\\
\end{array}
\left[
\begin{array}{ccc|c}
#a11 & #a12 & #a13 & #b1 \\
0 & #a22p & #a23p & #b2p \\
0 & 0 & 0 & #b3pp
\end{array}
\right]
\end{align*}

Da terceira equa??o conclui-se que o sistema $(S)$ n?o tem solu??es, ou seja, $\CS_$(S)=\emptyset$.


#Result:

\[
\CS_{(S)}=\emptyset
\]

#Verification:

set( \emptyset );