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
\( \color{red}A =
\begin{pmatrix}
-6 & -8 & 5 & 4 \\ 14 & 4 & 17 & 6 \\ -4 & -2 & 10 & -6 \\ 9 & 0 & -7 & 5\end{pmatrix}
\)
și
\( \color{blue}B =
\begin{pmatrix}
-1 & 10 & -6 & 15 \\ -8 & 12 & -1 & 7 \\ -2 & 16 & 10 & 16 \\ -5 & 16 & -10 & -2\end{pmatrix}
\)
este \( A+B = \)
exercițiu nou
Suma matricelor
\( \color{red}A =
\begin{pmatrix}
-6 & -8 & 5 & 4 \\ 14 & 4 & 17 & 6 \\ -4 & -2 & 10 & -6 \\ 9 & 0 & -7 & 5\end{pmatrix}
\)
și
\( \color{blue}B =
\begin{pmatrix}
-1 & 10 & -6 & 15 \\ -8 & 12 & -1 & 7 \\ -2 & 16 & 10 & 16 \\ -5 & 16 & -10 & -2\end{pmatrix}
\)
este
\( A+B = \) \( \begin{pmatrix}-7 & 2 & -1 & 19 \\ 6 & 16 & 16 & 13 \\ -6 & 14 & 20 & 10 \\ 4 & 16 & -17 & 3\end{pmatrix} \).
\( \color{orange} C \color{dimgray} = \color{red} A \color{dimgray} + \color{blue} B \color{dimgray} = \)
\( = \color{red}
\begin{pmatrix}
-6 & -8 & 5 & 4 \\ 14 & 4 & 17 & 6 \\ -4 & -2 & 10 & -6 \\ 9 & 0 & -7 & 5\end{pmatrix}
\)
\( + \color{blue}
\begin{pmatrix}
-1 & 10 & -6 & 15 \\ -8 & 12 & -1 & 7 \\ -2 & 16 & 10 & 16 \\ -5 & 16 & -10 & -2\end{pmatrix}
\color{dimgray} =
\)
\( =
\begin{pmatrix}
\color{red}-6 \color{dimgray} + \color{blue}(-1) & \color{red}-8 \color{dimgray} + \color{blue}10 & \color{red}5 \color{dimgray} + \color{blue}(-6) & \color{red}4 \color{dimgray} + \color{blue}15 \\ \color{red}14 \color{dimgray} + \color{blue}(-8) & \color{red}4 \color{dimgray} + \color{blue}12 & \color{red}17 \color{dimgray} + \color{blue}(-1) & \color{red}6 \color{dimgray} + \color{blue}7 \\ \color{red}-4 \color{dimgray} + \color{blue}(-2) & \color{red}-2 \color{dimgray} + \color{blue}16 & \color{red}10 \color{dimgray} + \color{blue}10 & \color{red}-6 \color{dimgray} + \color{blue}16 \\ \color{red}9 \color{dimgray} + \color{blue}(-5) & \color{red}0 \color{dimgray} + \color{blue}16 & \color{red}-7 \color{dimgray} + \color{blue}(-10) & \color{red}5 \color{dimgray} + \color{blue}(-2)\end{pmatrix} =
\)
\( =
\begin{pmatrix}
-6 - 1 & -8 + 10 & 5 - 6 & 4 + 15 \\ 14 - 8 & 4 + 12 & 17 - 1 & 6 + 7 \\ -4 - 2 & -2 + 16 & 10 + 10 & -6 + 16 \\ 9 - 5 & 0 + 16 & -7 - 10 & 5 - 2\end{pmatrix} =
\)
\( = \color{orange}
\begin{pmatrix}
-7 & 2 & -1 & 19 \\ 6 & 16 & 16 & 13 \\ -6 & 14 & 20 & 10 \\ 4 & 16 & -17 & 3\end{pmatrix}
\).
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