Question

Pergunta sobre matriz (em anexo) 

Answer 1

Olá, Carol.

$A^tX=B^t\Rightarrow\\\\\left(\begin{array}{ccc}2&3\\-1&4\\\end{array}\right)\cdot \left(\begin{array}{ccc}x_{11}\\x_{21}\\\end{array}\right)=\left(\begin{array}{ccc}2x_{11}+3x_{21}\\-x_{11}+4x_{21}\\\end{array}\right)=\left(\begin{array}{ccc}3\\9\\\end{array}\right)\Rightarrow\\\\\\\begin{cases}2x_{11}+3x_{21}=3\\-x_{11}+4x_{21}=9\,\,(\times2)\end{cases}\Rightarrow\\\\\\\begin{cases}2x_{11}+3x_{21}=3\\-2x_{11}+8x_{21}=18\end{cases}(+)\Rightarrow$

$11x_{21}=21\Rightarrow \boxed{x_{21}=\frac{21}{11}}\Rightarrow\\\\ 2x_{11}+3\cdot\frac{21}{11}=3\Rightarrow\\\\ 22x_{11}+63=33\Rightarrow\\\\ x_{11}=\frac{-30}{22}\Rightarrow\\\\ \boxed{x_{11}=-\frac{15}{11}}$

$\therefore \boxed{X=\left(\begin{array}{ccc} -\frac{15}{11} \\ \\ \frac{21}{11} \end{array}\right)}$