إذا كانت $\text{،}\underset{\_}{R}=\left[\begin{array}{cc}\begin{array}{rr}2& -1\\ 1& 3\end{array}& \end{array}\right] ,\underset{\_}{S}= \left[\begin{array}{cc}\begin{array}{rr}4& 6\\ -2& 5\end{array}& \end{array}\right],\underset{\_}{T}=\left[\begin{array}{cc}\begin{array}{ll}-3& 7\\ -4& 8\end{array}& \end{array}\right]$ فحدد ما إذا كان $(\underset{\_}{S}+\underset{\_}{T})\underset{\_}{R}=\underset{\_}{S}\underset{\_}{R}+\underset{\_}{T}\underset{\_}{R}$ صحيحة للمصفوفات المعطاة أم لا؟

$\begin{array}{rl}& (\underset{\_}{S}+\underset{\_}{T})\underset{\_}{R}=\left[\begin{array}{cc}\begin{array}{cc}15& 38\\ 1& 45\end{array}& \end{array}\right]\\ & \underset{\_}{S}\underset{\_}{R}+\underset{\_}{T}\underset{\_}{R}=\left[\begin{array}{cc}\begin{array}{cc}15& 38\\ 1& 45\end{array}& \end{array}\right]\\ & (\underset{\_}{S}+\underset{\_}{T})\underset{\_}{R}=\underset{\_}{S}\underset{\_}{R}+\underset{\_}{T}\underset{\_}{R}\end{array}$

نعم.

حل أسئلة تحقق من فهمك

1A)

${\underset{\_}{\mathit{A}}}_{4\times 6},{\underset{\_}{\mathit{B}}}_{6\times 2}$

4 $\times$ 2

2B)

${\underset{\_}{A}}_{3\times 2},{\underset{\_}{B}}_{3\times 2}$

غير معرفة.

2) إذا كانت $\underset{\_}{U}=\left[\begin{array}{cc}\begin{array}{rr}5& 9\\ -3& -2\end{array}& \end{array}\right] ,\underset{\_}{V}=\left[\begin{array}{cc}\begin{array}{ll}2& -1\\ 6& -5\end{array}& \end{array}\right]$ فأوجد $\underset{\_}{U}\underset{\_}{V}$.

$\begin{array}{r}\left[\begin{array}{cc}\begin{array}{cc}5\left(2\right)+9\left(6\right)& 5(-1)+9(-5)\\ (-3)\left(2\right)+(-2)\left(6\right)& (-3)(-1)+(-2)(-5)\end{array}& \end{array}\right]=\underset{\_}{U}\underset{\_}{V}\\ \\ \left[\begin{array}{cc}\begin{array}{cc}64& -50\\ -18& 13\end{array}& \end{array}\right]=\end{array}$

3) مبيعات: ارجع إلى فقرة لماذا؟ بداية الدرس واستعمل ضرب المصفوفات لتحديد سعر بيع الأقلام في كل شهر.

$\left[\begin{array}{cc}\begin{array}{cccc}153& 217& 197& 249\\ 12& 6& 7& 8\\ 82& 146& 102& 158\end{array}& \end{array}\right]\cdot \left[\begin{array}{cc}\begin{array}{l}1\\ 3\\ 2\end{array}& \end{array}\right]=\left[\begin{array}{llll}273& 527& 422& 433\end{array}\right]$

• شهر محرم 237.
• شهر صفر 527.
• شهر ربيع الأول 422.
• شهر ربيع الثاني 433.

4) إذا كانت $\underset{\_}{A}=\left[\begin{array}{cc}\begin{array}{ll}4& -1\\ 5& -2\end{array}& \end{array}\right] , \underset{\_}{B}=\left[\begin{array}{cc}\begin{array}{ll}-3& 6\\ -4& 5\end{array}& \end{array}\right]$ فهل $\underset{\_}{A}\underset{\_}{B}=\underset{\_}{B}\underset{\_}{A}$؟

$\begin{array}{r}\underset{\_}{A}\underset{\_}{B}=\left[\begin{array}{cc}\begin{array}{ll}-8& 19\\ -7& 20\end{array}& \end{array}\right],\underset{\_}{B}\underset{\_}{A}=\left[\begin{array}{cc}\begin{array}{cc}18& -9\\ 9& -6\end{array}& \end{array}\right]\\ \\ \underset{\_}{A}\underset{\_}{B}\ne \underset{\_}{B}\underset{\_}{A}\end{array}$

5) إذا كانت $\text{،}\underset{\_}{R}=\left[\begin{array}{cc}\begin{array}{rr}2& -1\\ 1& 3\end{array}& \end{array}\right] ,\underset{\_}{S}= \left[\begin{array}{cc}\begin{array}{rr}4& 6\\ -2& 5\end{array}& \end{array}\right],\underset{\_}{T}=\left[\begin{array}{cc}\begin{array}{ll}-3& 7\\ -4& 8\end{array}& \end{array}\right]$ فحدد ما إذا كان $(\underset{\_}{S}+\underset{\_}{T})\underset{\_}{R}=\underset{\_}{S}\underset{\_}{R}+\underset{\_}{T}\underset{\_}{R}$ صحيحة للمصفوفات المعطاة أم لا؟

$\begin{array}{rl}& (\underset{\_}{S}+\underset{\_}{T})\underset{\_}{R}=\left[\begin{array}{cc}\begin{array}{cc}15& 38\\ 1& 45\end{array}& \end{array}\right]\\ & \underset{\_}{S}\underset{\_}{R}+\underset{\_}{T}\underset{\_}{R}=\left[\begin{array}{cc}\begin{array}{cc}15& 38\\ 1& 45\end{array}& \end{array}\right]\\ & (\underset{\_}{S}+\underset{\_}{T})\underset{\_}{R}=\underset{\_}{S}\underset{\_}{R}+\underset{\_}{T}\underset{\_}{R}\end{array}$

نعم.