Question

resolva a equação matricial AX = B, dada as matrizes: A = [ 2 3 | -3 6 ] B = [ 5 3 | -4 13]

Answer 1

Oie, tudo bom?

$AX = B \\ \textstyle \begin{bmatrix} 2&3 \\ - 3&6 \end{bmatrix} \: . \: \textstyle \begin{bmatrix} a&b \\ c&d \end{bmatrix} = \textstyle \begin{bmatrix} 5&3 \\ - 4&13 \end{bmatrix} \\ \textstyle\begin{bmatrix} 2a + 3c&2b + 3d \\ - 3a + 6c&- 3b + 6d \end{bmatrix} = \textstyle\begin{bmatrix} 5&3 \\ - 4&13 \end{bmatrix}$

$2a + 3c = 5 \\ 2b + 3d = 3 \\ - 3a + 6c = - 4 \\ - 3b + 6d = 13$

$\begin{cases} 2a + 3c = 5 \\ - 3a + 6c = - 4 \end{cases} \\ \begin{cases} - 4a - 6c = - 10 \\ -3a + 6c = - 4 \end{cases} \\ - 7a = - 14 \: \: \: \: \: \: .( - 1) \\ 7a = 14 \\ a = \frac{14}{7} \\ \boxed{a = 2} \\ 2a + 3c = 5 \\ 2 \: . \: 2 + 3c = 5 \\ 4 + 3c = 5 \\ 3c = 5 - 4 \\ 3c = 1 \\ \boxed{c = \frac{1}{3} }$

$\begin{cases} 2b + 3d = 3\\ - 3b + 6d = 13\end{cases} \\ \begin{cases} - 4b - 6d = - 6\\ - 3b + 6d = 13\end{cases} \\ - 7b = 7 \: \: \: \: \: \: .( - 1) \\ 7b = - 7 \\ b = - \frac{7}{7} \\ \boxed{b = - 1} \\ 2b + 3d = 3 \\ 2 \: . \: ( - 1) + 3d = 3 \\ - 2 + 3d = 3 \\ 3d = 3 + 2 \\ 3d = 5 \\ \boxed{d = \frac{5}{3} }$

$\boxed{\textstyle x = \begin{bmatrix} 2& - 1\\ \frac{1}{3}&\frac{5}{3} \end{bmatrix}}$

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