2.8 Show that tridiagonal matrices A = with the properties a1 C1 b2 a2 C2 b3...

  

Transcribed Image Text:

2.8 Show that tridiagonal matrices A = with the properties a1 C1 b2 a2 C2 b3 a3 C3 bn-1 An-1 bn Cn-1 an - |aj|bj|cj|, bjcj 0, j = 2, ..., n 1, and |a1| > |c1| > 0 and |an| > |bn| > 0 are nonsingular. 2.8 Show that tridiagonal matrices A = with the properties a1 C1 b2 a2 C2 b3 a3 C3 bn-1 An-1 bn Cn-1 an - |aj|bj|cj|, bjcj 0, j = 2, ..., n 1, and |a1| > |c1| > 0 and |an| > |bn| > 0 are nonsingular.