确定a,b的值使得下列非齐次方程组有解,并求其解。ax1+bx2+2x3=1. (b-1)x2+x3=0. ax1+bx2+(1_b)x3=3-2b

2025-05-13 23:30:47
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回答1:

ax1+bx2+2x3=1,①
(b-1)x2+x3=0,②
ax1+bx2+(1-b)x3=3-2b,③
①-③,(b+1)x3=2(b-1),
方程有解,∴b≠-1,x3=2(b-1)/(b+1),
代入②,(b-1)x2+2(b-1)/(b+1)=0,
b=1时x2为任意数,b≠1时x2=-2/(b+1),
代入①,ax1+(2b-4)/(b+1)=1,
ax1=(5-b)/(b+1),
a=0,b=5时x1为任意数,a≠0时x1=(5-b)/[a(b+1)].