Question

k为何值时,线性方程组X1+X2+KX3=4 -X1+KX2+X3=K*K X1-X2+2X3=-4

Answer 1

增广矩阵 =

1 1 k 4

-1 k 1 k^2

1 -1 2 -4

r1-r3,r2+r3

0 2 k-2 8

0 k-1 3 k^2-4

1 -1 2 -4

r2*2,r2-(k-1)r1

0 2 k-2 8

0 0 (1+k)(4-k) 2k(k-4)

1 -1 2 -4

k≠-1 且 k≠4 时,方程组有唯一解.

k=-1 时,方程组无解.

k= 4 时,方程组有无穷多解.