Question

利用初等行变换求下列矩阵的列向量组的一个最大无关组,并把其余列向量用最大无关组 线性表示.

Answer 1

1 1 2 2 1

0 2 1 5 -1

2 0 3 -1 3

1 1 0 4 -1

r3-2r1,r4-r1

1 1 2 2 1

0 2 1 5 -1

0 -2 -1 -5 1

0 0 -2 2 -2

r3+r2,r4*(-1/2)

1 1 2 2 1

0 2 1 5 -1

0 0 0 0 0

0 0 1 -1 1

r1-2r4,r2-r4

1 1 0 4 -1

0 2 0 6 -2

0 0 0 0 0

0 0 1 -1 1

r2*(1/2)

1 1 0 4 -1

0 1 0 3 -1

0 0 0 0 0

0 0 1 -1 1

r1-r2,r3r4

1 0 0 1 0

0 1 0 3 -1

0 0 1 -1 1

0 0 0 0 0

极大无关组:a1,a2,a3

a4 = a1+3a2-a3

a5 = -a2 +a3