إذا كان $\underset{\_}{C}=\left[\begin{array}{cc}\begin{array}{rr}-4& -6\\ 12& -7\end{array}& \end{array}\right]\underset{\_}{B}=\left[\begin{array}{cc}\begin{array}{rr}8& -1\\ -2& 7\end{array}& \end{array}\right]\underset{\_}{A}=\left[\begin{array}{cc}\begin{array}{ll}6& -4\\ 3& -5\end{array}& \end{array}\right]$ فأوجد ناتج كل مما يأتي:

$\begin{array}{rl}4\left[\begin{array}{cc}\begin{array}{cc}8& -1\\ -2& 7\end{array}& \end{array}\right]-2& \left[\begin{array}{cc}\begin{array}{cc}6& -4\\ 3& -5\end{array}& \end{array}\right]=4\underset{\_}{B}-2\underset{\_}{A}\\ \left[\begin{array}{cc}\begin{array}{cc}4\cdot 8& 4\cdot (-1)\\ 4\cdot (-2)& 4\cdot 7\end{array}& \end{array}\right]-\left[\begin{array}{cc}\begin{array}{cc}2\cdot 6& 2\cdot (-4)\\ 2\cdot 3& 2\cdot (-5)\end{array}& \end{array}\right]& =\\ \left[\begin{array}{cc}\begin{array}{cc}32& -4\\ -8& 28\end{array}& \end{array}\right]-& \left[\begin{array}{cc}\begin{array}{cc}12& -8\\ 6& -10\end{array}& \end{array}\right]=\\ & \left[\begin{array}{cc}\begin{array}{cc}32-12& (-4)-(-8)\\ (-8)-6& 28-(-10)\end{array}& \end{array}\right]=\\ & \left[\begin{array}{cc}\begin{array}{cc}20& 4\\ -14& 38\end{array}& \end{array}\right]=\end{array}$

حل اسئلة تأكد

أوجد الناتج في كل مما يأتي إذا كان ذلك ممكناً:

1)

$\left[\begin{array}{lll}3& -5& 7\end{array}\right]=\left[\begin{array}{lll}-8& 2& 6\end{array}\right]+\left[\begin{array}{lll}11& -7& 1\end{array}\right]$

2)

$=\left[\begin{array}{lll}9& -8& 4\end{array}\right]+\left[\begin{array}{ll}12& 2\end{array}\right]$ غير ممكن.

3)

$\left[\begin{array}{cc}\begin{array}{cc}-2& 18\\ 11& 13\end{array}& \end{array}\right]=\left[\begin{array}{cc}\begin{array}{cc}7& -12\\ 15& 4\end{array}& \end{array}\right]-\left[\begin{array}{cc}\begin{array}{cc}9& 6\\ 4& -9\end{array}& \end{array}\right]$

4 )

$\left[\begin{array}{cc}\begin{array}{ccc}7& 31& -14\\ 1& -6& 2\end{array}& \end{array}\right]=\left[\begin{array}{cc}\begin{array}{ccc}5& 13& -6\\ 3& -17& 2\end{array}& \end{array}\right]-\left[\begin{array}{cc}\begin{array}{ccc}-2& -18& 8\\ 2& -11& 0\end{array}& \end{array}\right]$

أوجد الناتج في كل مما يأتي:

5)

$\left[\begin{array}{cc}\begin{array}{ccc}18& 12& 0\\ -6& 42& -24\\ -12& -18& 21\end{array}& \end{array}\right]=3\left[\begin{array}{cc}\begin{array}{ccc}6& 4& 0\\ -2& 14& -8\\ -4& -6& 7\end{array}& \end{array}\right]$

6)

$\left[\begin{array}{cc}\begin{array}{cccc}-90& 54& -12& -18\\ -36& 66& -84& 12\\ -24& 48& 60& -162\end{array}& \end{array}\right]=-6\left[\begin{array}{cc}\begin{array}{cccc}15& -9& 2& 3\\ 6& -11& 14& -2\\ 4& -8& -10& 27\end{array}& \end{array}\right]$

إذا كان $\underset{\_}{C}=\left[\begin{array}{cc}\begin{array}{rr}-4& -6\\ 12& -7\end{array}& \end{array}\right]\underset{\_}{B}=\left[\begin{array}{cc}\begin{array}{rr}8& -1\\ -2& 7\end{array}& \end{array}\right]\underset{\_}{A}=\left[\begin{array}{cc}\begin{array}{ll}6& -4\\ 3& -5\end{array}& \end{array}\right]$ فأوجد ناتج كل مما يأتي:

7)

$\begin{array}{rl}4\left[\begin{array}{cc}\begin{array}{cc}8& -1\\ -2& 7\end{array}& \end{array}\right]-2& \left[\begin{array}{cc}\begin{array}{cc}6& -4\\ 3& -5\end{array}& \end{array}\right]=4\underset{\_}{B}-2\underset{\_}{A}\\ \left[\begin{array}{cc}\begin{array}{cc}4\cdot 8& 4\cdot (-1)\\ 4\cdot (-2)& 4\cdot 7\end{array}& \end{array}\right]-\left[\begin{array}{cc}\begin{array}{cc}2\cdot 6& 2\cdot (-4)\\ 2\cdot 3& 2\cdot (-5)\end{array}& \end{array}\right]& =\\ \left[\begin{array}{cc}\begin{array}{cc}32& -4\\ -8& 28\end{array}& \end{array}\right]-& \left[\begin{array}{cc}\begin{array}{cc}12& -8\\ 6& -10\end{array}& \end{array}\right]=\\ & \left[\begin{array}{cc}\begin{array}{cc}32-12& (-4)-(-8)\\ (-8)-6& 28-(-10)\end{array}& \end{array}\right]=\\ & \left[\begin{array}{cc}\begin{array}{cc}20& 4\\ -14& 38\end{array}& \end{array}\right]=\end{array}$

8)

$\begin{array}{rl}-8\left[\begin{array}{cc}\begin{array}{cc}-4& -6\\ 12& -7\end{array}& \end{array}\right]+3& \left[\begin{array}{cc}\begin{array}{ll}6& -4\\ 3& -5\end{array}& \end{array}\right]=-8\underset{\_}{C}+3\underset{\_}{A}\\ \left[\begin{array}{cc}\begin{array}{cc}32& 48\\ -96& 56\end{array}& \end{array}\right]+\left[\begin{array}{cc}\begin{array}{cc}18& -12\\ 9& -15\end{array}& \end{array}\right]& =\\ \begin{array}{}\\ \end{array}& \left[\begin{array}{cc}\begin{array}{cc}50& 36\\ -87& 41\end{array}& \end{array}\right]=\end{array}$

9) درجات الحرارة: تبين المصفوفة L المعدل الشهري لدرجات الحرارة الصغرى (بالفهرنهايت) في مدينة ما وتبين المصفوفة H المعدل الشهري لدرجات الحرارة العظمى (بالفهرنهايت) في تلك المدينة.

$\underset{\_}{H}=\left[\begin{array}{cc}& \begin{array}{lll}39.9& 45.2& 55.3\\ 65.1& 74.0& 82.3\\ 85.9& 84.6& 78.1\\ 66.9& 54.5& 44.3\end{array}\end{array}\right]\underset{\_}{L}=\left[\begin{array}{cc}\begin{array}{lll}24.1& 27.7& 35.9\\ 44.1& 53.6& 62.2\\ 66.4& 64.9& 57.9\\ 46.4& 37.3& 28.4\end{array}& \end{array}\right]$

أوجد المصفوفة التي تمثل الفرق بين المعدل الشهري لدرجات الحرارة العظمى والمعدل الشهري لدرجات الحرارة الصغرى في تلك المدينة؟

$\begin{array}{r}\left[\begin{array}{cc}\begin{array}{lll}39.9& 45.2& 55.3\\ 65.1& 74.0& 82.3\\ 85.9& 84.6& 78.1\\ 66.9& 54.5& 44.3\end{array}& \end{array}\right]-\left[\begin{array}{cc}\begin{array}{ccc}24.1& 27.7& 35.9\\ 44.1& 53.6& 62.2\\ 66.4& 64.9& 57.9\\ 46.4& 37.3& 28.4\end{array}& \end{array}\right]=\\ \left[\begin{array}{cc}\begin{array}{ccc}15.8& 17.5& 19.4\\ 21& 20.4& 20.1\\ 19.5& 19.7& 20.2\\ 20.5& 17.2& 15.9\end{array}& \end{array}\right]=\end{array}$