有限数学 示例

Solve Using a Matrix by Elimination -25-9y-z=-16 , -15-15y-2z=26 , 20x+9y+z=6
, ,
解题步骤 1
Move variables to the left and constant terms to the right.
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解题步骤 1.1
将所有不包含变量的项移到等式右边。
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解题步骤 1.1.1
在等式两边都加上
解题步骤 1.1.2
相加。
解题步骤 1.2
将所有不包含变量的项移到等式右边。
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解题步骤 1.2.1
在等式两边都加上
解题步骤 1.2.2
相加。
解题步骤 2
Write the system as a matrix.
解题步骤 3
求行简化阶梯形矩阵。
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解题步骤 3.1
Swap with to put a nonzero entry at .
解题步骤 3.2
Multiply each element of by to make the entry at a .
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解题步骤 3.2.1
Multiply each element of by to make the entry at a .
解题步骤 3.2.2
化简
解题步骤 3.3
Multiply each element of by to make the entry at a .
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解题步骤 3.3.1
Multiply each element of by to make the entry at a .
解题步骤 3.3.2
化简
解题步骤 3.4
Perform the row operation to make the entry at a .
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解题步骤 3.4.1
Perform the row operation to make the entry at a .
解题步骤 3.4.2
化简
解题步骤 3.5
Multiply each element of by to make the entry at a .
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解题步骤 3.5.1
Multiply each element of by to make the entry at a .
解题步骤 3.5.2
化简
解题步骤 3.6
Perform the row operation to make the entry at a .
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解题步骤 3.6.1
Perform the row operation to make the entry at a .
解题步骤 3.6.2
化简
解题步骤 3.7
Perform the row operation to make the entry at a .
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解题步骤 3.7.1
Perform the row operation to make the entry at a .
解题步骤 3.7.2
化简
解题步骤 3.8
Perform the row operation to make the entry at a .
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解题步骤 3.8.1
Perform the row operation to make the entry at a .
解题步骤 3.8.2
化简
解题步骤 4
Use the result matrix to declare the final solution to the system of equations.
解题步骤 5
The solution is the set of ordered pairs that make the system true.