有限数学 示例

Solve Using a Matrix by Row Operations x+2y+z=72 , 2x+y+z=66 , 3x+y+2z=102 , p-60x-48y-42z=0
, , ,
解题步骤 1
Write the system as a matrix.
解题步骤 2
求行简化阶梯形矩阵。
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解题步骤 2.1
Swap with to put a nonzero entry at .
解题步骤 2.2
Multiply each element of by to make the entry at a .
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解题步骤 2.2.1
Multiply each element of by to make the entry at a .
解题步骤 2.2.2
化简
解题步骤 2.3
Perform the row operation to make the entry at a .
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解题步骤 2.3.1
Perform the row operation to make the entry at a .
解题步骤 2.3.2
化简
解题步骤 2.4
Perform the row operation to make the entry at a .
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解题步骤 2.4.1
Perform the row operation to make the entry at a .
解题步骤 2.4.2
化简
解题步骤 2.5
Multiply each element of by to make the entry at a .
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解题步骤 2.5.1
Multiply each element of by to make the entry at a .
解题步骤 2.5.2
化简
解题步骤 2.6
Perform the row operation to make the entry at a .
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解题步骤 2.6.1
Perform the row operation to make the entry at a .
解题步骤 2.6.2
化简
解题步骤 2.7
Multiply each element of by to make the entry at a .
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解题步骤 2.7.1
Multiply each element of by to make the entry at a .
解题步骤 2.7.2
化简
解题步骤 2.8
Perform the row operation to make the entry at a .
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解题步骤 2.8.1
Perform the row operation to make the entry at a .
解题步骤 2.8.2
化简
解题步骤 2.9
Perform the row operation to make the entry at a .
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解题步骤 2.9.1
Perform the row operation to make the entry at a .
解题步骤 2.9.2
化简
解题步骤 2.10
Perform the row operation to make the entry at a .
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解题步骤 2.10.1
Perform the row operation to make the entry at a .
解题步骤 2.10.2
化简
解题步骤 2.11
Perform the row operation to make the entry at a .
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解题步骤 2.11.1
Perform the row operation to make the entry at a .
解题步骤 2.11.2
化简
解题步骤 2.12
Perform the row operation to make the entry at a .
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解题步骤 2.12.1
Perform the row operation to make the entry at a .
解题步骤 2.12.2
化简
解题步骤 2.13
Perform the row operation to make the entry at a .
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解题步骤 2.13.1
Perform the row operation to make the entry at a .
解题步骤 2.13.2
化简
解题步骤 3
Use the result matrix to declare the final solution to the system of equations.
解题步骤 4
The solution is the set of ordered pairs that make the system true.