Question

线性代数讨论-2X1+X2+X3=-2 X1-2X2+X3=K X1+X2-2X3=K^2的解的情况,有唯一解,无解和无

Answer 1

A =

[ -2,1,1,-2]

[ 1,-2,1,k]

[ 1,1,-2,k^2]

交换第1,3行

A =

[ 1,1,-2,k^2]

[ 1,-2,1,k]

[ -2,1,1,-2]

r2-r1;r3+2r1

A =

[ 1,1,-2,k^2]

[ 0,-3,3,k - k^2]

[ 0,3,-3,2*k^2 - 2]

r3+r2

A =

[ 1,1,-2,k^2]

[ 0,-3,3,k - k^2]

[ 0,0,0,k^2 + k - 2]

所以k无论取何值,都不会有唯一解

当k=1或k=-2时,有无穷多解

当k≠1或k≠-2时,无解