Analysis: To determine the value of a parameter, the determinant is often equal to 0.

Because the equations have solutions, r(A)=r(A, b).

Since A has only two columns, R (a) = R (a, b).

So determinant |A, b| = 0.

[ 1, - 1, 2]

[ 1, 2, 1]

[ 3，k， 1]

= k- 12

So k = 12.