Under what condition on the parameter h will the sweep for SLAE be stable?

Question

Mathematics

They asked a problem here, but I'm not sure where to start, I thought about the diagonal predominance, but I'm not sure.
Under what condition on the parameter h will the sweep for SLAE be stable if the system matrix has the form:

.
      (-2           1-ha       0            0      ........      0             0)
      (1+ha      -2            1-ha      0      ........      0             0)
А = (0            1+ha       -2        1-ha   ........      0             0)
      (...............................................................................)
      (0            0            0            0       ........      1+ha      -2)

a is a given positive number.
It turns out that if I use diagonal dominance, then I can deduce from the inequality:
|-2| > |1+ha| + |1-ha|.
Are my thoughts in the right direction?

Answer 1

Cramer's method, it seems. The matrix is ​​reduced to a triangular form, in which the determinant depends only on the diagonal.