Question

高等数学线性代数第2大题，详细步骤，不要省略，谢谢。

Answer 1

A =
[ 1, 1, 1, 1]
[ -1, 2, 3, a]
[ 1, 4, 9, a^2]
[ -1, 8, 27, a^3]

r2 = r2 + r1; r3 = r3 - r1; r4 = r4 + r1
=
[ 1, 1, 1, 1]
[ 0, 3, 4, a + 1]
[ 0, 3, 8, a^2 - 1]
[ 0, 9, 28, a^3 + 1]

r3 = r3 - r2; r4 = r4 -3r2
=
[ 1, 1, 1, 1]
[ 0, 3, 4, a + 1]
[ 0, 0, 4, a^2 - a - 2]
[ 0, 0, 16, a^3 - 3*a - 2]

r4 = r4 - 4r3
=
[ 1, 1, 1, 1]
[ 0, 3, 4, a + 1]
[ 0, 0, 4, a^2 - a - 2]
[ 0, 0, 0, a^3 - 4*a^2 + a + 6]

当 a^3 - 4*a^2 + a + 6 = 0
即 a = -1 或 a = 2 或 a = 3 时
方程组有解，且有唯一解
当 a= -1 时 解为：[ 1 0 0]
当 a= 2 时 解为：[ 0 1 0]
当 a= 3 时 解为：[0 0 1]

当删除第4个方程时，有解，且解唯一