问a , b为何值时,线性方程组 有唯一解、无解、 有无穷多解?并求出有无穷多解时的通解.
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a不等于1时,a、b取值可得唯一解
x1=-1+b/(a-1),x2=1-2b/(a-1),x3=(1+b)/(a-1).x4=-1/(a-1);
a=1,b不等于-1时,无解
因2式与3式矛盾;
a=1,b=-1时,方程组变为:
x1+x2+x3+x4=0,,,,x2+2x3+2x4=1,,,,-x2-2x3-2x4=-1,,,,3x1+2x2+x3+x4=-1
简化下变为x1+x2+x3+x4=0,,,,x2+2x3+2x4=1
x1=x3+x4-1,x2=1-2(x3+x4),x3无穷,x4无穷
x1=-1+b/(a-1),x2=1-2b/(a-1),x3=(1+b)/(a-1).x4=-1/(a-1);
a=1,b不等于-1时,无解
因2式与3式矛盾;
a=1,b=-1时,方程组变为:
x1+x2+x3+x4=0,,,,x2+2x3+2x4=1,,,,-x2-2x3-2x4=-1,,,,3x1+2x2+x3+x4=-1
简化下变为x1+x2+x3+x4=0,,,,x2+2x3+2x4=1
x1=x3+x4-1,x2=1-2(x3+x4),x3无穷,x4无穷
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