Modify the Cholesky Algorithm as suggested in the text so that it can be used to solve linear systems, and use the modified algorithm to solve the linear systems in Exercise 7.
In Exercise 7
a. 2x1 − x2 = 3,
−x1 + 2x2 − x3 = −3,
− x2 + 2x3 = 1.
b. 4x1 + x2 + x3 + x4 = 0.65,
x1 + 3x2 − x3 + x4 = 0.05,
x1 − x2 + 2x3 = 0,
x1 + x2 + 2x4 = 0.5.
c. 4x1 + x2 − x3 = 7,
x1 + 3x2 − x3 = 8,
−x1 − x2 + 5x3 + 2x4 = −4,
2x3 + 4x4 = 6.
d. 6x1 + 2x2 + x3 − x4 = 0,
2x1 + 4x2 + x3 = 7,
x1 + x2 + 4x3 − x4 = −1,
−x1 − x3 + 3x4 = −2.