3) D etermine a) 2A-B= b) 4A+2B= c) A^t-B^t A=vert } -3&5&2 6&4&8 vert B=vert } -8&-9&12 45&6&-3 vert

Para resolver as operações com as matrizes \( A \) e \( B \), primeiro precisamos calcular a matriz transposta \( A^t \) e \( B^t \).<br /><br />Dada:<br />\[ A = \begin{pmatrix} -3 & 5 & 2 \\ 6 & 4 & 8 \end{pmatrix} \]<br />\[ B = \begin{pmatrix} -8 & -9 & 12 \\ 45 & 6 & -3 \end{pmatrix} \]<br /><br />Calculando as transpostas:<br />\[ A^t = \begin{pmatrix} -3 & 6 \\ 5 & 4 \\ 2 & 8 \end{pmatrix} \]<br />\[ B^t = \begin{pmatrix} -8 & 45 \\ -9 & 6 \\ 12 & -3 \end{pmatrix} \]<br /><br />Agora, podemos realizar as operações:<br /><br />a) \( 2A - B \)<br /><br />\[ 2A = 2 \times \begin{pmatrix} -3 & 5 & 2 \\ 6 & 4 & 8 \end{pmatrix} = \begin{pmatrix} -6 & 10 & 4 \\ 12 & 8 & 16 \end{pmatrix} \]<br /><br />\[ 2A - B = \begin{pmatrix} -6 & 10 & 4 \\ 12 & 8 & 16 \end{pmatrix} - \begin{pmatrix} -8 & -9 & 12 \\ 45 & 6 & -3 \end{pmatrix} = \begin{pmatrix} -6 + 8 & 10 + 9 & 4 - 12 \\ 12 - 45 & 8 - 6 & 16 + 3 \end{pmatrix} = \begin{pmatrix} 2 & 19 & -8 \\ -33 & 2 & 19 \end{pmatrix} \]<br /><br />b) \( 4A + 2B \)<br /><br />\[ 4A = 4 \times \begin{pmatrix} -3 & 5 & 2 \\ 6 & 4 & 8 \end{pmatrix} = \begin{pmatrix} -12 & 20 & 8 \\ 24 & 16 & 32 \end{pmatrix} \]<br /><br />\[ 2B = 2 \times \begin{pmatrix} -8 & -9 & 12 \\ 45 & 6 & -3 \end{pmatrix} = \begin{pmatrix} -16 & -18 & 24 \\ 90 & 12 & -6 \end{pmatrix} \]<br /><br />\[ 4A + 2B = \begin{pmatrix} -12 & 20 & 8 \\ 24 & 16 & 32 \end{pmatrix} + \begin{pmatrix} -16 & -18 & 24 \\ 90 & 12 & -6 \end{pmatrix} = \begin{pmatrix} -12 - 16 & 20 - 18 & 8 + 24 \\ 24 + 90 & 16 + 12 & 32 - 6 \end{pmatrix} = \begin{pmatrix} -28 & 2 & 32 \\ 114 & 28 & 26 \end{pmatrix} \]<br /><br />c) \( A^t - B^t \)<br /><br />\[ A^t - B^t = \begin{pmatrix} -3 & 6 \\ 5 & 4 \\ 2 & 8 \end{pmatrix} - \begin{pmatrix} -8 & 45 \\ -9 & 6 \\ 12 & -3 \end{pmatrix} = \begin{pmatrix} -3 + 8 & 6 - 45 \\ 5 + 9 & 4 - 6 \\ 2 - 12 & 8 + 3 \end{pmatrix} = \begin{pmatrix} 5 & -39 \\ 14 & -2 \\ -10 & 11 \end{pmatrix} \]<br /><br />Portanto, as respostas são:<br /><br />a) \( 2A - B = \begin{pmatrix} 2 & 19 & -8 \\ -33 & 2 & 19 \end{pmatrix} \)<br /><br />b) \( 4A + 2B = \begin{pmatrix} -28 & 2 & 32 \\ 114 & 28 & 26 \end{pmatrix} \)<br /><br />c) \( A^t - B^t = \begin{pmatrix} 5 & -39 \\ 14 & -2 \\ -10 & 11 \end{pmatrix} \)