الجبر الخطي الأمثلة

المسائل الشائعة
الجبر الخطي
بسّط المصفوفة 3[[0,0,2],[3,1,0],[0,-2,4]]-2[[0,2,1],[3,0,5],[7,-6,0]]+8[[1,-1,2],[3,4,5],[0,1,-1]]-4[[0,25,12,5],[6,75,8,75,7,5],[-3,5,3.5,-1]]
3[0023100-24]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]3⎡⎢⎣0023100−24⎤⎥⎦−2⎡⎢⎣0213057−60⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
Step 1
اضرب 33 في كل عنصر من عناصر المصفوفة.
[3⋅03⋅03⋅23⋅33⋅13⋅03⋅03⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣3⋅03⋅03⋅23⋅33⋅13⋅03⋅03⋅−23⋅4⎤⎥⎦−2⎡⎢⎣0213057−60⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
Step 2
بسّط كل عنصر في المصفوفة.
انقر لعرض المزيد من الخطوات...
أعِد ترتيب 3⋅03⋅0.
[03⋅03⋅23⋅33⋅13⋅03⋅03⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣03⋅03⋅23⋅33⋅13⋅03⋅03⋅−23⋅4⎤⎥⎦−2⎡⎢⎣0213057−60⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب 3⋅03⋅0.
[003⋅23⋅33⋅13⋅03⋅03⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣003⋅23⋅33⋅13⋅03⋅03⋅−23⋅4⎤⎥⎦−2⎡⎢⎣0213057−60⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب 3⋅23⋅2.
[0063⋅33⋅13⋅03⋅03⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0063⋅33⋅13⋅03⋅03⋅−23⋅4⎤⎥⎦−2⎡⎢⎣0213057−60⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب 3⋅33⋅3.
[00693⋅13⋅03⋅03⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣00693⋅13⋅03⋅03⋅−23⋅4⎤⎥⎦−2⎡⎢⎣0213057−60⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب 3⋅13⋅1.
[006933⋅03⋅03⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣006933⋅03⋅03⋅−23⋅4⎤⎥⎦−2⎡⎢⎣0213057−60⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب 3⋅03⋅0.
[0069303⋅03⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0069303⋅03⋅−23⋅4⎤⎥⎦−2⎡⎢⎣0213057−60⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب 3⋅03⋅0.
[00693003⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣00693003⋅−23⋅4⎤⎥⎦−2⎡⎢⎣0213057−60⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب 3⋅-23⋅−2.
[0069300-63⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−63⋅4⎤⎥⎦−2⎡⎢⎣0213057−60⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب 3⋅43⋅4.
[0069300-612]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦−2⎡⎢⎣0213057−60⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
[0069300-612]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦−2⎡⎢⎣0213057−60⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
Step 3
اضرب -2−2 في كل عنصر من عناصر المصفوفة.
[0069300-612]+[-2⋅0-2⋅2-2⋅1-2⋅3-2⋅0-2⋅5-2⋅7-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦+⎡⎢⎣−2⋅0−2⋅2−2⋅1−2⋅3−2⋅0−2⋅5−2⋅7−2⋅−6−2⋅0⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
Step 4
بسّط كل عنصر في المصفوفة.
انقر لعرض المزيد من الخطوات...
أعِد ترتيب -2⋅0−2⋅0.
[0069300-612]+[0-2⋅2-2⋅1-2⋅3-2⋅0-2⋅5-2⋅7-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦+⎡⎢⎣0−2⋅2−2⋅1−2⋅3−2⋅0−2⋅5−2⋅7−2⋅−6−2⋅0⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب -2⋅2−2⋅2.
[0069300-612]+[0-4-2⋅1-2⋅3-2⋅0-2⋅5-2⋅7-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦+⎡⎢⎣0−4−2⋅1−2⋅3−2⋅0−2⋅5−2⋅7−2⋅−6−2⋅0⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب -2⋅1−2⋅1.
[0069300-612]+[0-4-2-2⋅3-2⋅0-2⋅5-2⋅7-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦+⎡⎢⎣0−4−2−2⋅3−2⋅0−2⋅5−2⋅7−2⋅−6−2⋅0⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب -2⋅3−2⋅3.
[0069300-612]+[0-4-2-6-2⋅0-2⋅5-2⋅7-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦+⎡⎢⎣0−4−2−6−2⋅0−2⋅5−2⋅7−2⋅−6−2⋅0⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب -2⋅0−2⋅0.
[0069300-612]+[0-4-2-60-2⋅5-2⋅7-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦+⎡⎢⎣0−4−2−60−2⋅5−2⋅7−2⋅−6−2⋅0⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب -2⋅5−2⋅5.
[0069300-612]+[0-4-2-60-10-2⋅7-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦+⎡⎢⎣0−4−2−60−10−2⋅7−2⋅−6−2⋅0⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب -2⋅7−2⋅7.
[0069300-612]+[0-4-2-60-10-14-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦+⎡⎢⎣0−4−2−60−10−14−2⋅−6−2⋅0⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب -2⋅-6−2⋅−6.
[0069300-612]+[0-4-2-60-10-1412-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦+⎡⎢⎣0−4−2−60−10−1412−2⋅0⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب -2⋅0−2⋅0.
[0069300-612]+[0-4-2-60-10-14120]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦+⎡⎢⎣0−4−2−60−10−14120⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
[0069300-612]+[0-4-2-60-10-14120]+8[1-1234501-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦+⎡⎢⎣0−4−2−60−10−14120⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
Step 5
اضرب 88 في كل عنصر من عناصر المصفوفة.
[0069300-612]+[0-4-2-60-10-14120]+[8⋅18⋅-18⋅28⋅38⋅48⋅58⋅08⋅18⋅-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦+⎡⎢⎣0−4−2−60−10−14120⎤⎥⎦+⎡⎢⎣8⋅18⋅−18⋅28⋅38⋅48⋅58⋅08⋅18⋅−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
Step 6
بسّط كل عنصر في المصفوفة.
انقر لعرض المزيد من الخطوات...
أعِد ترتيب 8⋅18⋅1.
[0069300-612]+[0-4-2-60-10-14120]+[88⋅-18⋅28⋅38⋅48⋅58⋅08⋅18⋅-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦+⎡⎢⎣0−4−2−60−10−14120⎤⎥⎦+⎡⎢⎣88⋅−18⋅28⋅38⋅48⋅58⋅08⋅18⋅−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب 8⋅-18⋅−1.
[0069300-612]+[0-4-2-60-10-14120]+[8-88⋅28⋅38⋅48⋅58⋅08⋅18⋅-1]-4[02512567587575-353.5-1]⎡⎢⎣0069300−612⎤⎥⎦+⎡⎢⎣0−4−2−60−10−14120⎤⎥⎦+⎡⎢⎣8−88⋅28⋅38⋅48⋅58⋅08⋅18⋅−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
أعِد ترتيب 8⋅2.
[0069300-612]+[0-4-2-60-10-14120]+[8-8168⋅38⋅48⋅58⋅08⋅18⋅-1]-4[02512567587575-353.5-1]
أعِد ترتيب 8⋅3.
[0069300-612]+[0-4-2-60-10-14120]+[8-816248⋅48⋅58⋅08⋅18⋅-1]-4[02512567587575-353.5-1]
أعِد ترتيب 8⋅4.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624328⋅58⋅08⋅18⋅-1]-4[02512567587575-353.5-1]
أعِد ترتيب 8⋅5.
[0069300-612]+[0-4-2-60-10-14120]+[8-8162432408⋅08⋅18⋅-1]-4[02512567587575-353.5-1]
أعِد ترتيب 8⋅0.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008⋅18⋅-1]-4[02512567587575-353.5-1]
أعِد ترتيب 8⋅1.
[0069300-612]+[0-4-2-60-10-14120]+[8-816243240088⋅-1]-4[02512567587575-353.5-1]
أعِد ترتيب 8⋅-1.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]-4[02512567587575-353.5-1]
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]-4[02512567587575-353.5-1]
Step 7
اضرب -4 في كل عنصر من عناصر المصفوفة.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[-4⋅0-4⋅25-4⋅12-4⋅5-4⋅6-4⋅75-4⋅8-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
Step 8
بسّط كل عنصر في المصفوفة.
انقر لعرض المزيد من الخطوات...
أعِد ترتيب -4⋅0.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-4⋅25-4⋅12-4⋅5-4⋅6-4⋅75-4⋅8-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
أعِد ترتيب -4⋅25.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-4⋅12-4⋅5-4⋅6-4⋅75-4⋅8-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
أعِد ترتيب -4⋅12.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-4⋅5-4⋅6-4⋅75-4⋅8-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
أعِد ترتيب -4⋅5.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-4⋅6-4⋅75-4⋅8-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
أعِد ترتيب -4⋅6.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-4⋅75-4⋅8-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
أعِد ترتيب -4⋅75.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-4⋅8-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
أعِد ترتيب -4⋅8.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
أعِد ترتيب -4⋅75.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
أعِد ترتيب -4⋅7.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
أعِد ترتيب -4⋅5.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-20-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
أعِد ترتيب -4⋅-3.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-4⋅5-4⋅3.5-4⋅-1]
أعِد ترتيب -4⋅5.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-4⋅3.5-4⋅-1]
أعِد ترتيب -4⋅3.5.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-14-4⋅-1]
أعِد ترتيب -4⋅-1.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Step 9
اجمع العناصر المتناظرة.
[0+00-46-29-63+00-100-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Step 10
بسّط كل عنصر من عناصر المصفوفة [0+00-46-29-63+00-100-14-6+1212+0].
انقر لعرض المزيد من الخطوات...
بسّط 0+0.
[00-46-29-63+00-100-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط 0-4.
[0-46-29-63+00-100-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط 6-2.
[0-449-63+00-100-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط 9-6.
[0-4433+00-100-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط 3+0.
[0-44330-100-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط 0-10.
[0-4433-100-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط 0-14.
[0-4433-10-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط -6+12.
[0-4433-10-14612+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط 12+0.
[0-4433-10-14612]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
[0-4433-10-14612]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Step 11
اجمع العناصر المتناظرة.
[0+8-4-84+163+243+32-10+40-14+06+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Step 12
بسّط كل عنصر من عناصر المصفوفة [0+8-4-84+163+243+32-10+40-14+06+812-8].
انقر لعرض المزيد من الخطوات...
بسّط 0+8.
[8-4-84+163+243+32-10+40-14+06+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط -4-8.
[8-124+163+243+32-10+40-14+06+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط 4+16.
[8-12203+243+32-10+40-14+06+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط 3+24.
[8-1220273+32-10+40-14+06+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط 3+32.
[8-12202735-10+40-14+06+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط -10+40.
[8-1220273530-14+06+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط -14+0.
[8-1220273530-146+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط 6+8.
[8-1220273530-141412-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
بسّط 12-8.
[8-1220273530-14144]+[0-100-48-20-24-300-32-300-28-2012-20-144]
[8-1220273530-14144]+[0-100-48-20-24-300-32-300-28-2012-20-144]
 [x2  12  √π  ∫xdx ]