Matematică >> matrice și determinanți >> 1
\( \color{orange} C \color{dimgray} \in \textit{M}_{m,n}(\mathbb{C}) \), \( \color{orange} C \color{dimgray} = \color{red} A \color{dimgray} + \color{blue} B \), prin
\( \color{orange} c\color{dimgray}_{ij} = \color{red} a\color{dimgray}_{ij} \color{dimgray} + \color{blue} b\color{dimgray}_{ij} \), \( i \in \{1, 2, ..., m \} \), \( j \in \{1, 2, ..., n \} \).
suma matricelor
\( \color{red}A = \begin{pmatrix} 8 & -5 & 7 & 0 \\ 2 & 14 & -9 & -3 \end{pmatrix} \)
și
\( \color{blue}B = \begin{pmatrix} -1 & +4 & 2 & -7 \\ -18 & 8 & -6 & 9 \end{pmatrix} \)
este:
\( \color{orange} C \color{dimgray} = \color{red} A \color{dimgray} + \color{blue} B \color{dimgray} = \)
\( = \color{red} \begin{pmatrix} 8 & -5 & 7 & 0 \\ 2 & 14 & -9 & -3 \end{pmatrix} \color{dimgray} + \color{blue} \begin{pmatrix} -1 & +4 & 2 & -7 \\ -18 & 8 & -6 & 9 \end{pmatrix} \color{dimgray} = \)
\( = \begin{pmatrix} \color{red}8 \color{dimgray}+( \color{blue}-1 \color{dimgray}) & \color{red}-5 \color{dimgray}+( \color{blue}+4 \color{dimgray}) & \color{red}7 \color{dimgray}+ \color{blue}2 & \color{red}0 \color{dimgray}+( \color{blue}-7 \color{dimgray}) \\ \color{red}2 \color{dimgray}+( \color{blue}-18 \color{dimgray}) & \color{red}14 \color{dimgray}+ \color{blue}8 & \color{red}-9 \color{dimgray}+( \color{blue}-6 \color{dimgray}) & \color{red}-3 \color{dimgray}+ \color{blue}9 \end{pmatrix} = \)
\( = \begin{pmatrix} 8-1 & -5+4 & 7+2 & 0-7 \\ 2-18 & 14+8 & -9-6 & -3+9 \end{pmatrix} = \)
\( = \color{orange} \begin{pmatrix} 7 & -1 & 9 & -7 \\ -16 & 22 & -15 & 6 \end{pmatrix} \).
Suma matricelor
\( \color{red}A =
\begin{pmatrix}
5 & -2 & 16 \\ 10 & 0 & 0 \\ -10 & 12 & 8\end{pmatrix}
\)
și
\( \color{blue}B =
\begin{pmatrix}
17 & 7 & -2 \\ 8 & 9 & 10 \\ 11 & 6 & -1\end{pmatrix}
\)
este \( A+B = \)
exercițiu nou
Suma matricelor
\( \color{red}A =
\begin{pmatrix}
5 & -2 & 16 \\ 10 & 0 & 0 \\ -10 & 12 & 8\end{pmatrix}
\)
și
\( \color{blue}B =
\begin{pmatrix}
17 & 7 & -2 \\ 8 & 9 & 10 \\ 11 & 6 & -1\end{pmatrix}
\)
este
\( A+B = \) \( \begin{pmatrix}22 & 5 & 14 \\ 18 & 9 & 10 \\ 1 & 18 & 7\end{pmatrix} \).
\( \color{orange} C \color{dimgray} = \color{red} A \color{dimgray} + \color{blue} B \color{dimgray} = \)
\( = \color{red}
\begin{pmatrix}
5 & -2 & 16 \\ 10 & 0 & 0 \\ -10 & 12 & 8\end{pmatrix}
\)
\( + \color{blue}
\begin{pmatrix}
17 & 7 & -2 \\ 8 & 9 & 10 \\ 11 & 6 & -1\end{pmatrix}
\color{dimgray} =
\)
\( =
\begin{pmatrix}
\color{red}5 \color{dimgray} + \color{blue}17 & \color{red}-2 \color{dimgray} + \color{blue}7 & \color{red}16 \color{dimgray} + \color{blue}(-2) \\ \color{red}10 \color{dimgray} + \color{blue}8 & \color{red}0 \color{dimgray} + \color{blue}9 & \color{red}0 \color{dimgray} + \color{blue}10 \\ \color{red}-10 \color{dimgray} + \color{blue}11 & \color{red}12 \color{dimgray} + \color{blue}6 & \color{red}8 \color{dimgray} + \color{blue}(-1)\end{pmatrix} =
\)
\( =
\begin{pmatrix}
5 + 17 & -2 + 7 & 16 - 2 \\ 10 + 8 & 0 + 9 & 0 + 10 \\ -10 + 11 & 12 + 6 & 8 - 1\end{pmatrix} =
\)
\( = \color{orange}
\begin{pmatrix}
22 & 5 & 14 \\ 18 & 9 & 10 \\ 1 & 18 & 7\end{pmatrix}
\).
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