Question

线性代数求解设a1=(1;1;1;4;3),a2=(1;-1;3;-2;1),a3=(2;1;3;5;5).a4=(3;

Answer 1

解: (a1,a2,a3,a4)=

1 1 2 3

1 -1 1 1

1 3 3 5

4 -2 5 6

3 1 5 7

r2-r1,r3-r1,r4-4r1,r5-3r1

1 1 2 3

0 -2 -1 -2

0 2 1 2

0 -6 -3 -6

0 -2 -1 -2

r1-2r3,r2+r3,r4+3r3,r5+r3

1 -3 0 -1

0 0 0 0

0 2 1 2

0 0 0 0

0 0 0 0

所以向量组的秩为2, a1,a3是向量组的一个极大无关组

a2 = -3a1+2a3, a4 = -a1+2a3.