Determine which matrices in Exercise 2 are tri diagonal and positive definite. Repeat Exercise 2 for these matrices using the optimal choice of ω.
In Exercise 2
a. 4x1 + x2 − x3 = 5,
−x1 + 3x2 + x3 = −4,
2x1 + 2x2 + 5x3 = 1.
b. −2x1+ x2 + 1/2 x3 = 4,
x1−2x2 - 1/2 x3 = −4,
x2 + 2x3 = 0.
c. 4x1 + x2 − x3 + x4 = −2,
x1 + 4x2 − x3 − x4 = −1,
−x1 − x2 + 5x3 + x4 = 0,
x1 − x2 + x3 + 3x4 = 1.
d. 4x1 − x2 = 0,
−x1 + 4x2 − x3 = 5,
− x2 + 4x3 = 0,
+ 4x4 − x5 = 6,
− x4 + 4x5 − x6 = −2,
− x5 + 4x6 = 6.