الجبر الخطي الأمثلة

أوجد الصفرية [[1,-1,3],[6,7,-3],[9,4,6]]
[1-1367-3946]
خطوة 1
Nullity is the dimension of the null space, which is the same as the number of free variables in the system after row reducing. The free variables are the columns without pivot positions.
خطوة 2
أوجِد الصيغة الدرجية المختزلة صفيًا.
انقر لعرض المزيد من الخطوات...
خطوة 2.1
Perform the row operation R2=R2-6R1 to make the entry at 2,1 a 0.
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خطوة 2.1.1
Perform the row operation R2=R2-6R1 to make the entry at 2,1 a 0.
[1-136-617-6-1-3-63946]
خطوة 2.1.2
بسّط R2.
[1-13013-21946]
[1-13013-21946]
خطوة 2.2
Perform the row operation R3=R3-9R1 to make the entry at 3,1 a 0.
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خطوة 2.2.1
Perform the row operation R3=R3-9R1 to make the entry at 3,1 a 0.
[1-13013-219-914-9-16-93]
خطوة 2.2.2
بسّط R3.
[1-13013-21013-21]
[1-13013-21013-21]
خطوة 2.3
Multiply each element of R2 by 113 to make the entry at 2,2 a 1.
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خطوة 2.3.1
Multiply each element of R2 by 113 to make the entry at 2,2 a 1.
[1-130131313-2113013-21]
خطوة 2.3.2
بسّط R2.
[1-1301-2113013-21]
[1-1301-2113013-21]
خطوة 2.4
Perform the row operation R3=R3-13R2 to make the entry at 3,2 a 0.
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خطوة 2.4.1
Perform the row operation R3=R3-13R2 to make the entry at 3,2 a 0.
[1-1301-21130-13013-131-21-13(-2113)]
خطوة 2.4.2
بسّط R3.
[1-1301-2113000]
[1-1301-2113000]
خطوة 2.5
Perform the row operation R1=R1+R2 to make the entry at 1,2 a 0.
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خطوة 2.5.1
Perform the row operation R1=R1+R2 to make the entry at 1,2 a 0.
[1+0-1+113-211301-2113000]
خطوة 2.5.2
بسّط R1.
[10181301-2113000]
[10181301-2113000]
[10181301-2113000]
خطوة 3
The pivot positions are the locations with the leading 1 in each row. The pivot columns are the columns that have a pivot position.
Pivot Positions: a11 and a22
Pivot Columns: 1 and 2
خطوة 4
The nullity is the number of columns without a pivot position in the row reduced matrix.
1
[1-1367-3946]
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