一道线代题目求教
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B = (β1, β2, β3, β4) =
[ 1 -1 1 1]
[ 0 1 0 1]
[ 1 1 1 3]
[-1 0 0 -1]
初等行变换为
[ 1 -1 1 1]
[ 0 1 0 1]
[ 0 2 0 2]
[ 0 -1 1 0]
初等行变换为
[ 1 0 1 2]
[ 0 1 0 1]
[ 0 0 0 0]
[ 0 0 1 1]
初等行变换为
[ 1 0 0 1]
[ 0 1 0 1]
[ 0 0 1 1]
[ 0 0 0 0]
r(β1, β2, β3, β4) = 3, β1, β2, β3 是一个极大线性无关组，
β4 = β1+β2+β3
[ 1 -1 1 1]
[ 0 1 0 1]
[ 1 1 1 3]
[-1 0 0 -1]
初等行变换为
[ 1 -1 1 1]
[ 0 1 0 1]
[ 0 2 0 2]
[ 0 -1 1 0]
初等行变换为
[ 1 0 1 2]
[ 0 1 0 1]
[ 0 0 0 0]
[ 0 0 1 1]
初等行变换为
[ 1 0 0 1]
[ 0 1 0 1]
[ 0 0 1 1]
[ 0 0 0 0]
r(β1, β2, β3, β4) = 3, β1, β2, β3 是一个极大线性无关组，
β4 = β1+β2+β3
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