给定齐次线性方程组{X1+X2+X3+X4=0,X1+KX2+X3-X4=0,X1+X2+KX3-X4=0},问(1)
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给定齐次线性方程组{X1+X2+X3+X4=0,X1+KX2+X3-X4=0,X1+X2+KX3-X4=0},问(1) 当K满足什么条件时,方程组
![给定齐次线性方程组{X1+X2+X3+X4=0,X1+KX2+X3-X4=0,X1+X2+KX3-X4=0},问(1)](/uploads/image/z/5833506-66-6.jpg?t=%E7%BB%99%E5%AE%9A%E9%BD%90%E6%AC%A1%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84%7BX1%2BX2%2BX3%2BX4%3D0%2CX1%2BKX2%2BX3-X4%3D0%2CX1%2BX2%2BKX3-X4%3D0%7D%2C%E9%97%AE%EF%BC%881%EF%BC%89)
系数矩阵 A =
1 1 1 1
1 k 1 -1
1 1 k -1
r2-r1,r3-r1
1 1 1 1
0 k-1 0 -2
0 0 k-1 -2
(1) k≠1时,r(A)=3,
方程组的基础解系中含 4-r(A) = 1 个解向量.
(2) k=1时,方程组无解.
1 1 1 1
1 k 1 -1
1 1 k -1
r2-r1,r3-r1
1 1 1 1
0 k-1 0 -2
0 0 k-1 -2
(1) k≠1时,r(A)=3,
方程组的基础解系中含 4-r(A) = 1 个解向量.
(2) k=1时,方程组无解.
给定齐次线性方程组{X1+X2+X3+X4=0,X1+KX2+X3-X4=0,X1+X2+KX3-X4=0},问(1)
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