Question

3.求向量组 a1=(1,1,1,3)^T，a2 =(-1,-3,5,1)^T，a3 =(3,2,

Answer 1

问：3.求向量组 a1=(1,1,1,3)^T，a2 =(-1,-3,5,1)^T，a3 =(3,2,

答：亲亲您好，非常高兴能回答您的问题:解: (a1,a2,a3,a4,a) =1 -1 3 -2 41 -3 2 -6 11 5 -1 10 63 1 p+2 p 10r3-r1-r2-r3, r3-r2,r2-r11 -1 3 -2 40 -2 -1 -4 -30 8 -3 16 50 0 p-2 p-2 -1r3+4r21 -1 3 -2 40 -2 -1 -4 -30 0 -7 0 -70 0 p-2 p-2 -1r3*(-1/7),r1-3r3,r2+r3,r4-(p-1)r31 -1 0 -2 10 -2 0 -4 -20 0 1 0 10 0 0 p-2 -p+1r2*(-1/2),r1+r21 0 0 0 20 1 0 2 10 0 1 0 10 0 0 p-2 -p+1当p=2时, a1,a2,a3,a4线性相关, r(a1,a2,a3,a4)=3, a1,a2,a3 是一个极大无关组.当p≠2时, a1,a2,a3,a4线性无关.此时, (a1,a2,a3,a4,a) -->...r4*[1/(p-2)], r2-2r41 0 0 0 20 1 0 0 (3p-4)/(p-2)0 0 1 0 10 0 0 1 -(p-1)/(p-2)a=2a1+[(3p-4)/(p-2)]a2+a3-[(p-1)/(p-2)]a4.