Modify the LDLt Factorization Algorithm as suggested in the text so that it can be used to solve linear systems. Use the modified algorithm to solve the following linear systems.
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.