A =
[ 1, 2, 1, 3]
[ -1, 1, -1, 0]
[ 0, 5, -2, 7]
[ 4, 6, 0, k]
化为行最简矩阵：
A =
[ 1, 2, 1, 3]
[ 0, 1, 0, 1]
[ 0, 0, -1, 1]
[ 0, 0, 0, 3*k - 42]
当3*k - 42 = 0时线性相关
即当 k = 14 时，向量组线性相关
当 k = 14 时
A =
1 2 1 3
-1 1 -1 0
0 5 -2 7
4 6 0 14
化为行最简矩阵：
1 0 0 2
0 1 0 1
0 0 1 -1
0 0 0 0
∴极大无关组：a1,a2,a3
a4 = 2a1 + a2 - a3
答题不易，请及时采纳，谢谢！