الجبر الخطي الأمثلة

$3 [\begin{array}{c} 0 & 0 & 2 \\ 3 & 1 & 0 \\ 0 & - 2 & 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Step 1

اضرب $3$ في كل عنصر من عناصر المصفوفة.

$[\begin{array}{c} 3 \cdot 0 & 3 \cdot 0 & 3 \cdot 2 \\ 3 \cdot 3 & 3 \cdot 1 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Step 2

بسّط كل عنصر في المصفوفة.

انقر لعرض المزيد من الخطوات...

أعِد ترتيب $3 \cdot 0$ .

$[\begin{array}{c} 0 & 3 \cdot 0 & 3 \cdot 2 \\ 3 \cdot 3 & 3 \cdot 1 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $3 \cdot 0$ .

$[\begin{array}{c} 0 & 0 & 3 \cdot 2 \\ 3 \cdot 3 & 3 \cdot 1 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $3 \cdot 2$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 3 \cdot 3 & 3 \cdot 1 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $3 \cdot 3$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 \cdot 1 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $3 \cdot 1$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $3 \cdot 0$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 3 \cdot 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $3 \cdot 0$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & 3 \cdot - 2 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $3 \cdot - 2$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 3 \cdot 4 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $3 \cdot 4$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] - 2 [\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 5 \\ 7 & - 6 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Step 3

اضرب $- 2$ في كل عنصر من عناصر المصفوفة.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} - 2 \cdot 0 & - 2 \cdot 2 & - 2 \cdot 1 \\ - 2 \cdot 3 & - 2 \cdot 0 & - 2 \cdot 5 \\ - 2 \cdot 7 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Step 4

بسّط كل عنصر في المصفوفة.

انقر لعرض المزيد من الخطوات...

أعِد ترتيب $- 2 \cdot 0$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 2 \cdot 2 & - 2 \cdot 1 \\ - 2 \cdot 3 & - 2 \cdot 0 & - 2 \cdot 5 \\ - 2 \cdot 7 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $- 2 \cdot 2$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \cdot 1 \\ - 2 \cdot 3 & - 2 \cdot 0 & - 2 \cdot 5 \\ - 2 \cdot 7 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $- 2 \cdot 1$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 2 \cdot 3 & - 2 \cdot 0 & - 2 \cdot 5 \\ - 2 \cdot 7 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $- 2 \cdot 3$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & - 2 \cdot 0 & - 2 \cdot 5 \\ - 2 \cdot 7 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $- 2 \cdot 0$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 2 \cdot 5 \\ - 2 \cdot 7 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $- 2 \cdot 5$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 2 \cdot 7 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $- 2 \cdot 7$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & - 2 \cdot - 6 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $- 2 \cdot - 6$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & - 2 \cdot 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $- 2 \cdot 0$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + 8 [\begin{array}{c} 1 & - 1 & 2 \\ 3 & 4 & 5 \\ 0 & 1 & - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Step 5

اضرب $8$ في كل عنصر من عناصر المصفوفة.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 \cdot 1 & 8 \cdot - 1 & 8 \cdot 2 \\ 8 \cdot 3 & 8 \cdot 4 & 8 \cdot 5 \\ 8 \cdot 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Step 6

بسّط كل عنصر في المصفوفة.

انقر لعرض المزيد من الخطوات...

أعِد ترتيب $8 \cdot 1$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & 8 \cdot - 1 & 8 \cdot 2 \\ 8 \cdot 3 & 8 \cdot 4 & 8 \cdot 5 \\ 8 \cdot 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $8 \cdot - 1$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 8 \cdot 2 \\ 8 \cdot 3 & 8 \cdot 4 & 8 \cdot 5 \\ 8 \cdot 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $8 \cdot 2$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 8 \cdot 3 & 8 \cdot 4 & 8 \cdot 5 \\ 8 \cdot 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $8 \cdot 3$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 8 \cdot 4 & 8 \cdot 5 \\ 8 \cdot 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $8 \cdot 4$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 8 \cdot 5 \\ 8 \cdot 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $8 \cdot 5$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 8 \cdot 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $8 \cdot 0$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 \cdot 1 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $8 \cdot 1$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & 8 \cdot - 1 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

أعِد ترتيب $8 \cdot - 1$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] - 4 [\begin{array}{c} 0 & 25 & 12 & 5 \\ 6 & 75 & 8 & 75 & 7 & 5 \\ - 3 & 5 & 3.5 & - 1 \end{array}]$

Step 7

اضرب $- 4$ في كل عنصر من عناصر المصفوفة.

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} - 4 \cdot 0 & - 4 \cdot 25 & - 4 \cdot 12 & - 4 \cdot 5 \\ - 4 \cdot 6 & - 4 \cdot 75 & - 4 \cdot 8 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

Step 8

بسّط كل عنصر في المصفوفة.

انقر لعرض المزيد من الخطوات...

أعِد ترتيب $- 4 \cdot 0$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 4 \cdot 25 & - 4 \cdot 12 & - 4 \cdot 5 \\ - 4 \cdot 6 & - 4 \cdot 75 & - 4 \cdot 8 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

أعِد ترتيب $- 4 \cdot 25$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 4 \cdot 12 & - 4 \cdot 5 \\ - 4 \cdot 6 & - 4 \cdot 75 & - 4 \cdot 8 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

أعِد ترتيب $- 4 \cdot 12$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 4 \cdot 5 \\ - 4 \cdot 6 & - 4 \cdot 75 & - 4 \cdot 8 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

أعِد ترتيب $- 4 \cdot 5$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 4 \cdot 6 & - 4 \cdot 75 & - 4 \cdot 8 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

أعِد ترتيب $- 4 \cdot 6$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 4 \cdot 75 & - 4 \cdot 8 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

أعِد ترتيب $- 4 \cdot 75$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 4 \cdot 8 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

أعِد ترتيب $- 4 \cdot 8$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 4 \cdot 75 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

أعِد ترتيب $- 4 \cdot 75$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 4 \cdot 7 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

أعِد ترتيب $- 4 \cdot 7$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 4 \cdot 5 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

أعِد ترتيب $- 4 \cdot 5$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ - 4 \cdot - 3 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

أعِد ترتيب $- 4 \cdot - 3$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 4 \cdot 5 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

أعِد ترتيب $- 4 \cdot 5$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 4 \cdot 3.5 & - 4 \cdot - 1 \end{array}]$

أعِد ترتيب $- 4 \cdot 3.5$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & - 4 \cdot - 1 \end{array}]$

أعِد ترتيب $- 4 \cdot - 1$ .

$[\begin{array}{c} 0 & 0 & 6 \\ 9 & 3 & 0 \\ 0 & - 6 & 12 \end{array}] + [\begin{array}{c} 0 & - 4 & - 2 \\ - 6 & 0 & - 10 \\ - 14 & 12 & 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Step 9

اجمع العناصر المتناظرة.

$[\begin{array}{c} 0 + 0 & 0 - 4 & 6 - 2 \\ 9 - 6 & 3 + 0 & 0 - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Step 10

بسّط كل عنصر من عناصر المصفوفة $[\begin{array}{c} 0 + 0 & 0 - 4 & 6 - 2 \\ 9 - 6 & 3 + 0 & 0 - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}]$ .

انقر لعرض المزيد من الخطوات...

بسّط $0 + 0$ .

$[\begin{array}{c} 0 & 0 - 4 & 6 - 2 \\ 9 - 6 & 3 + 0 & 0 - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $0 - 4$ .

$[\begin{array}{c} 0 & - 4 & 6 - 2 \\ 9 - 6 & 3 + 0 & 0 - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $6 - 2$ .

$[\begin{array}{c} 0 & - 4 & 4 \\ 9 - 6 & 3 + 0 & 0 - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $9 - 6$ .

$[\begin{array}{c} 0 & - 4 & 4 \\ 3 & 3 + 0 & 0 - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $3 + 0$ .

$[\begin{array}{c} 0 & - 4 & 4 \\ 3 & 3 & 0 - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $0 - 10$ .

$[\begin{array}{c} 0 & - 4 & 4 \\ 3 & 3 & - 10 \\ 0 - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $0 - 14$ .

$[\begin{array}{c} 0 & - 4 & 4 \\ 3 & 3 & - 10 \\ - 14 & - 6 + 12 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $- 6 + 12$ .

$[\begin{array}{c} 0 & - 4 & 4 \\ 3 & 3 & - 10 \\ - 14 & 6 & 12 + 0 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $12 + 0$ .

$[\begin{array}{c} 0 & - 4 & 4 \\ 3 & 3 & - 10 \\ - 14 & 6 & 12 \end{array}] + [\begin{array}{c} 8 & - 8 & 16 \\ 24 & 32 & 40 \\ 0 & 8 & - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Step 11

اجمع العناصر المتناظرة.

$[\begin{array}{c} 0 + 8 & - 4 - 8 & 4 + 16 \\ 3 + 24 & 3 + 32 & - 10 + 40 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

Step 12

بسّط كل عنصر من عناصر المصفوفة $[\begin{array}{c} 0 + 8 & - 4 - 8 & 4 + 16 \\ 3 + 24 & 3 + 32 & - 10 + 40 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}]$ .

انقر لعرض المزيد من الخطوات...

بسّط $0 + 8$ .

$[\begin{array}{c} 8 & - 4 - 8 & 4 + 16 \\ 3 + 24 & 3 + 32 & - 10 + 40 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $- 4 - 8$ .

$[\begin{array}{c} 8 & - 12 & 4 + 16 \\ 3 + 24 & 3 + 32 & - 10 + 40 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $4 + 16$ .

$[\begin{array}{c} 8 & - 12 & 20 \\ 3 + 24 & 3 + 32 & - 10 + 40 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $3 + 24$ .

$[\begin{array}{c} 8 & - 12 & 20 \\ 27 & 3 + 32 & - 10 + 40 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $3 + 32$ .

$[\begin{array}{c} 8 & - 12 & 20 \\ 27 & 35 & - 10 + 40 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $- 10 + 40$ .

$[\begin{array}{c} 8 & - 12 & 20 \\ 27 & 35 & 30 \\ - 14 + 0 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $- 14 + 0$ .

$[\begin{array}{c} 8 & - 12 & 20 \\ 27 & 35 & 30 \\ - 14 & 6 + 8 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $6 + 8$ .

$[\begin{array}{c} 8 & - 12 & 20 \\ 27 & 35 & 30 \\ - 14 & 14 & 12 - 8 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$

بسّط $12 - 8$ .

$[\begin{array}{c} 8 & - 12 & 20 \\ 27 & 35 & 30 \\ - 14 & 14 & 4 \end{array}] + [\begin{array}{c} 0 & - 100 & - 48 & - 20 \\ - 24 & - 300 & - 32 & - 300 & - 28 & - 20 \\ 12 & - 20 & - 14 & 4 \end{array}]$