线性代数 示例

求解最简化梯阵形式 [[1,1,0],[1,0,1],[1,0,1],[2,1,0],[2,1,0]]
[110101101210210]⎢ ⎢ ⎢ ⎢ ⎢ ⎢110101101210210⎥ ⎥ ⎥ ⎥ ⎥ ⎥
解题步骤 1
Perform the row operation R2=R2-R1 to make the entry at 2,1 a 0.
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解题步骤 1.1
Perform the row operation R2=R2-R1 to make the entry at 2,1 a 0.
[1101-10-11-0101210210]
解题步骤 1.2
化简 R2
[1100-11101210210]
[1100-11101210210]
解题步骤 2
Perform the row operation R3=R3-R1 to make the entry at 3,1 a 0.
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解题步骤 2.1
Perform the row operation R3=R3-R1 to make the entry at 3,1 a 0.
[1100-111-10-11-0210210]
解题步骤 2.2
化简 R3
[1100-110-11210210]
[1100-110-11210210]
解题步骤 3
Perform the row operation R4=R4-2R1 to make the entry at 4,1 a 0.
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解题步骤 3.1
Perform the row operation R4=R4-2R1 to make the entry at 4,1 a 0.
[1100-110-112-211-210-20210]
解题步骤 3.2
化简 R4
[1100-110-110-10210]
[1100-110-110-10210]
解题步骤 4
Perform the row operation R5=R5-2R1 to make the entry at 5,1 a 0.
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解题步骤 4.1
Perform the row operation R5=R5-2R1 to make the entry at 5,1 a 0.
[1100-110-110-102-211-210-20]
解题步骤 4.2
化简 R5
[1100-110-110-100-10]
[1100-110-110-100-10]
解题步骤 5
Multiply each element of R2 by -1 to make the entry at 2,2 a 1.
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解题步骤 5.1
Multiply each element of R2 by -1 to make the entry at 2,2 a 1.
[110-0--1-110-110-100-10]
解题步骤 5.2
化简 R2
[11001-10-110-100-10]
[11001-10-110-100-10]
解题步骤 6
Perform the row operation R3=R3+R2 to make the entry at 3,2 a 0.
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解题步骤 6.1
Perform the row operation R3=R3+R2 to make the entry at 3,2 a 0.
[11001-10+0-1+111-10-100-10]
解题步骤 6.2
化简 R3
[11001-10000-100-10]
[11001-10000-100-10]
解题步骤 7
Perform the row operation R4=R4+R2 to make the entry at 4,2 a 0.
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解题步骤 7.1
Perform the row operation R4=R4+R2 to make the entry at 4,2 a 0.
[11001-10000+0-1+110-10-10]
解题步骤 7.2
化简 R4
[11001-100000-10-10]
[11001-100000-10-10]
解题步骤 8
Perform the row operation R5=R5+R2 to make the entry at 5,2 a 0.
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解题步骤 8.1
Perform the row operation R5=R5+R2 to make the entry at 5,2 a 0.
[11001-100000-10+0-1+110-1]
解题步骤 8.2
化简 R5
[11001-100000-100-1]
[11001-100000-100-1]
解题步骤 9
Swap R4 with R3 to put a nonzero entry at 3,3.
[11001-100-100000-1]
解题步骤 10
Multiply each element of R3 by -1 to make the entry at 3,3 a 1.
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解题步骤 10.1
Multiply each element of R3 by -1 to make the entry at 3,3 a 1.
[11001-1-0-0--100000-1]
解题步骤 10.2
化简 R3
[11001-100100000-1]
[11001-100100000-1]
解题步骤 11
Perform the row operation R5=R5+R3 to make the entry at 5,3 a 0.
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解题步骤 11.1
Perform the row operation R5=R5+R3 to make the entry at 5,3 a 0.
[11001-10010000+00+0-1+11]
解题步骤 11.2
化简 R5
[11001-1001000000]
[11001-1001000000]
解题步骤 12
Perform the row operation R2=R2+R3 to make the entry at 2,3 a 0.
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解题步骤 12.1
Perform the row operation R2=R2+R3 to make the entry at 2,3 a 0.
[1100+01+0-1+11001000000]
解题步骤 12.2
化简 R2
[110010001000000]
[110010001000000]
解题步骤 13
Perform the row operation R1=R1-R2 to make the entry at 1,2 a 0.
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解题步骤 13.1
Perform the row operation R1=R1-R2 to make the entry at 1,2 a 0.
[1-01-10-0010001000000]
解题步骤 13.2
化简 R1
[100010001000000]
[100010001000000]
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