Perform only two steps of the conjugate gradient method with C = C−1 = I on each of the following linear systems. Compare the results in parts (b) and (c) to the results obtained in parts (b) and (c) of Exercise 1 of Section 7.3 and Exercise 1 of Section 7.4.
a. 3x1 − x2 + x3 = 1,
−x1 + 6x2 + 2x3 = 0,
x1 + 2x2 + 7x3 = 4.
b. 10x1 − x2 = 9,
−x1 + 10x2 − 2x3 = 7,
− 2x2 + 10x3 = 6.
c. 10x1 + 5x2 = 6,
5x1 + 10x2 − 4x3 = 25,
− 4x2 + 8x3 − x4 = −11,
− x3 + 5x4 = −11.
d. 4x1 + x2 − x3 + x4 = −2,
x1 + 4x2 − x3 − x4 = −1,
−x1 − x2 + 5x3 + x4 = 0,
x1 − x2 + x3 + 3x4 = 1.
e. 4x1 + x2 + x3 + x5 = 6,
x1 + 3x2 + x3 + x4 = 6,
x1 + x2 + 5x3 − x4 − x5 = 6,
x2 − x3 + 4x4 = 6,
x1 − x3+ +4x5 = 6.
f. 4x1 − x2 − x4 = 0,
−x1 + 4x2 − x3 − x5 = 5,
− x2 + 4x3 − x6 = 0,
−x1 + 4x4 − x5 = 6,
− x2 − x4 + 4x5 − x6 = −2,
− x3 − x5 + 4x6 = 6.