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
\( \color{red}A =
\begin{pmatrix}
11 & 19 & 0 & 13 \\ -7 & -7 & 18 & 8 \\ 8 & -4 & -3 & -1 \\ 10 & 16 & 6 & -9\end{pmatrix}
\)
și
\( \color{blue}B =
\begin{pmatrix}
4 & 15 & 7 & -8 \\ 5 & -2 & 16 & 15 \\ 10 & 12 & 4 & -7 \\ 4 & 8 & -4 & 13\end{pmatrix}
\)
este \( A+B = \)
exercițiu nou
Suma matricelor
\( \color{red}A =
\begin{pmatrix}
11 & 19 & 0 & 13 \\ -7 & -7 & 18 & 8 \\ 8 & -4 & -3 & -1 \\ 10 & 16 & 6 & -9\end{pmatrix}
\)
și
\( \color{blue}B =
\begin{pmatrix}
4 & 15 & 7 & -8 \\ 5 & -2 & 16 & 15 \\ 10 & 12 & 4 & -7 \\ 4 & 8 & -4 & 13\end{pmatrix}
\)
este
\( A+B = \) \( \begin{pmatrix}15 & 34 & 7 & 5 \\ -2 & -9 & 34 & 23 \\ 18 & 8 & 1 & -8 \\ 14 & 24 & 2 & 4\end{pmatrix} \).
\( \color{orange} C \color{dimgray} = \color{red} A \color{dimgray} + \color{blue} B \color{dimgray} = \)
\( = \color{red}
\begin{pmatrix}
11 & 19 & 0 & 13 \\ -7 & -7 & 18 & 8 \\ 8 & -4 & -3 & -1 \\ 10 & 16 & 6 & -9\end{pmatrix}
\)
\( + \color{blue}
\begin{pmatrix}
4 & 15 & 7 & -8 \\ 5 & -2 & 16 & 15 \\ 10 & 12 & 4 & -7 \\ 4 & 8 & -4 & 13\end{pmatrix}
\color{dimgray} =
\)
\( =
\begin{pmatrix}
\color{red}11 \color{dimgray} + \color{blue}4 & \color{red}19 \color{dimgray} + \color{blue}15 & \color{red}0 \color{dimgray} + \color{blue}7 & \color{red}13 \color{dimgray} + \color{blue}(-8) \\ \color{red}-7 \color{dimgray} + \color{blue}5 & \color{red}-7 \color{dimgray} + \color{blue}(-2) & \color{red}18 \color{dimgray} + \color{blue}16 & \color{red}8 \color{dimgray} + \color{blue}15 \\ \color{red}8 \color{dimgray} + \color{blue}10 & \color{red}-4 \color{dimgray} + \color{blue}12 & \color{red}-3 \color{dimgray} + \color{blue}4 & \color{red}-1 \color{dimgray} + \color{blue}(-7) \\ \color{red}10 \color{dimgray} + \color{blue}4 & \color{red}16 \color{dimgray} + \color{blue}8 & \color{red}6 \color{dimgray} + \color{blue}(-4) & \color{red}-9 \color{dimgray} + \color{blue}13\end{pmatrix} =
\)
\( =
\begin{pmatrix}
11 + 4 & 19 + 15 & 0 + 7 & 13 - 8 \\ -7 + 5 & -7 - 2 & 18 + 16 & 8 + 15 \\ 8 + 10 & -4 + 12 & -3 + 4 & -1 - 7 \\ 10 + 4 & 16 + 8 & 6 - 4 & -9 + 13\end{pmatrix} =
\)
\( = \color{orange}
\begin{pmatrix}
15 & 34 & 7 & 5 \\ -2 & -9 & 34 & 23 \\ 18 & 8 & 1 & -8 \\ 14 & 24 & 2 & 4\end{pmatrix}
\).
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