x11+x2C2+.+xnCn=0XB1+x2B2+.+X,nBn=0 a1k1+41X2+.+41mXn=0 21+022++42nXn=0 21七1+22X2+.+42mXn=0 411+a12火2++41nn=0 0m火1+0m2七2+.+0mXn=0 0m火1+m2X2+.+amXn=0 同样的对另外两种行换得到类似的结论
同样的对另外两种行变换得到类似的结论。 0 x1 1 + x2 2 ++ xn n = 0 x1 1 + x2 2 ++ xn n = + + + = + + + = + + + = 0 0 0 1 1 2 2 21 1 22 2 2 11 1 12 2 1 m m mn n n n n n a x a x a x a x a x a x a x a x a x + + + = + + + = + + + = 0 0 0 1 1 2 2 11 1 12 2 1 21 1 22 2 2 m m mn n n n n n a x a x a x a x a x a x a x a x a x
A=[a,a2,.,an]→[B,B2,.,Bn]=B 对矩阵做第二种行变换后其列向量组 XC%+X202+.+XnCn=0 XB+x2+.+xnBn=0 a+a2X2+.+ann=0 4+a12X2++a1nXn=0 2+a222++a2mXn=0 kax+ka2x2++kanx=0 am+am22+.+Amnn=0 ami+am2x2+.+AmnXn=0
0 x1 1 + x2 2 ++ xn n = 0 x1 1 + x2 2 ++ xn n = + + + = + + + = + + + = 0 0 0 1 1 2 2 2 1 1 2 2 2 2 1 1 1 1 2 2 1 m m mn n n n n n a x a x a x a x a x a x a x a x a x + + + = + + + = + + + = 0 0 0 1 1 2 2 2 1 1 2 2 2 2 1 1 1 1 2 2 1 m m m n n n n n n a x a x a x k a x k a x k a x a x a x a x 对矩阵做第二种行变换后其列向量组 A = 1 ,2 , ,n →1 ,2 , ,n = B
A=[a,a2,.,a]→[B,B2,.,pn]=B 对矩阵做第三种行变换后其列向量组 x01+X202+.+xnan=0xB+x2B2+.+xnBn=0 r ak+a12x2+.+anXn=0 (au+ka)x++(ain+kan)x =0 41+a2X2+.+a2nn=0 a21+a22X3++a2mn=0 aml+am22+.+Amnn=0 amam2amnx=0
0 x1 1 + x2 2 ++ xn n = 0 x1 1 + x2 2 ++ xn n = + + + = + + + = + + + = 0 0 0 1 1 2 2 2 1 1 2 2 2 2 1 1 1 1 2 2 1 m m mn n n n n n a x a x a x a x a x a x a x a x a x + + + = + + + = + + + + = 0 0 ( ) ( ) 0 1 1 2 2 2 1 1 2 2 2 2 1 1 2 1 1 1 2 m m mn n n n n n n a x a x a x a x a x a x a k a x a k a x A = 1 ,2 , ,n →1 ,2 , ,n = B 对矩阵做第三种行变换后其列向量组