求这道线性代数题怎么做？
1个回答
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A = [α1 α2 α3 α4 β] =
[1 1 1 1 1]
[1 1 -1 -1 2]
[1 -1 1 -1 1]
[1 -1 -1 1 1]
初等行变换为
[1 1 1 1 1]
[0 0 -2 -2 1]
[0 -2 0 -2 0]
[0 -2 -2 0 0]
初等行变换为
[1 0 1 0 1]
[0 1 0 1 0]
[0 0 -2 -2 1]
[0 0 -2 2 0]
初等行变换为
[1 0 0 1 1]
[0 1 0 1 0]
[0 0 1 -1 0]
[0 0 0 -4 1]
初等行变换为
[1 0 0 0 5/4]
[0 1 0 0 1/4]
[0 0 1 0 -1/4]
[0 0 0 1 -1/4]
β = (5/4)α1 + (1/4)α2 - (1/4)α3 - (1/4)α4
[1 1 1 1 1]
[1 1 -1 -1 2]
[1 -1 1 -1 1]
[1 -1 -1 1 1]
初等行变换为
[1 1 1 1 1]
[0 0 -2 -2 1]
[0 -2 0 -2 0]
[0 -2 -2 0 0]
初等行变换为
[1 0 1 0 1]
[0 1 0 1 0]
[0 0 -2 -2 1]
[0 0 -2 2 0]
初等行变换为
[1 0 0 1 1]
[0 1 0 1 0]
[0 0 1 -1 0]
[0 0 0 -4 1]
初等行变换为
[1 0 0 0 5/4]
[0 1 0 0 1/4]
[0 0 1 0 -1/4]
[0 0 0 1 -1/4]
β = (5/4)α1 + (1/4)α2 - (1/4)α3 - (1/4)α4
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