将线性方程组
{3x1+x2-2x3=1,
{x1-x2=3,
{3x1+x2+2x3=5
写成矩阵形式:AX=B,并求A-1和X
原方程组变形为 (3 1 -2 (x1 1 -1 0 x2 3 1 2) x3) = (1 3 5) 因为 |A|=-1-6≠0,所以 A可逆 又A11=-2,A12=-2,A13=4,A21=-4,A22=12,A23=0,A31 =-2,A32=-2,A33=-4 所以 A-1=(1/|A|)A*=-(1/16) (-2 -4 -2 -2 12 -2 4 0 -4) = (1/8 1/4 1/8 1/8 -(3/4) 1/8 -(1/4) 0 1/4) 所以 X=A-1=B (1/8 1/4 1/8 1/8 -(3/4) 1/8 -(1/4) 0 1/4) (3 5 3) = (3/2 -(3/2) 1 )