例2判断向量组α =(1,-2,3), α, =(2,1,0), α, =(1,-7,9)是否线性无关？若线性相关，求一组非零数k,kz,kg,使k,a +k,αz +k,α=0.解：设k,α,+k,αz+k,α=0，即有方程组k+2k,+k,=0{k, = -3k3-2k,+k,-7k,=0，解之得，ks为任意数(k, =k)3k +9kg=0所以 αi,αz,α线性相关。令 k,=l，则有k, =-3,k, =1,k, =1, 使 k,α, +k,α, +k,α, = 083.3线性相关性区区§3.3 线性相关性 例2 判断向量组 是否线性无关？若线性相关，求一组非零数 1 2 3    = − = = − (1, 2,3), (2,1,0), (1, 7,9) 1 2 3 k k k ,,, 使 1 1 2 2 3 3 k k k    + + = 0. 解： 1 1 2 2 3 3 设 k k k    + + = 0, 即有方程组 1 2 3 1 2 3 1 3 2 0 2 7 0 , 3 9 0 k k k k k k k k  + + =  − + − =  + =   1 3 2 3 3 , k k k k = − 解之得 = 1 2 3 k k k = − = = 3, 1, 1, 3 k 为任意数 所以    1 2 3 , , 线性相关. 令 3 k = 1, 则有 使 1 1 2 2 3 3 k k k    + + = 0