الجبر الخطي الأمثلة

أوجد صيغة الصف المنخفض للمصفوفة [[a,b,1,0],[c,d,0,1]]
[ab10cd01]
خطوة 1
Multiply each element of R1 by 1a to make the entry at 1,1 a 1.
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خطوة 1.1
Multiply each element of R1 by 1a to make the entry at 1,1 a 1.
[aaba1a0acd01]
خطوة 1.2
بسّط R1.
[1ba1a0cd01]
[1ba1a0cd01]
خطوة 2
Perform the row operation R2=R2-cR1 to make the entry at 2,1 a 0.
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خطوة 2.1
Perform the row operation R2=R2-cR1 to make the entry at 2,1 a 0.
[1ba1a0c-c1d-cba0-c1a1-c0]
خطوة 2.2
بسّط R2.
[1ba1a00d-bca-ca1]
[1ba1a00d-bca-ca1]
خطوة 3
Multiply each element of R2 by 1d-bca to make the entry at 2,2 a 1.
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خطوة 3.1
Multiply each element of R2 by 1d-bca to make the entry at 2,2 a 1.
[1ba1a00d-bcad-bcad-bca-cad-bca1d-bca]
خطوة 3.2
بسّط R2.
[1ba1a001-cda-bcada-bc]
[1ba1a001-cda-bcada-bc]
خطوة 4
Perform the row operation R1=R1-baR2 to make the entry at 1,2 a 0.
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خطوة 4.1
Perform the row operation R1=R1-baR2 to make the entry at 1,2 a 0.
[1-ba0ba-ba11a-ba(-cda-bc)0-baada-bc01-cda-bcada-bc]
خطوة 4.2
بسّط R1.
[101a+bca(da-bc)-bda-bc01-cda-bcada-bc]
[101a+bca(da-bc)-bda-bc01-cda-bcada-bc]
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