For each of the systems in Exercise 1.1.1. write down the coefficient matrix A and the vectors x and b.
Exercise 1.1.1
Solve the following systems of linear equations by reducing to triangular form and then using Back Substitution.
(a) x - y = 7
x + 2y = 3
(b) 6u + v = 5
3u - 2v = 5
(c) p + q - r = 0
2p - q + 3r = 3
-p - q = 6
(d) 2u - v + 2w = 2
- u - v + 3w = 1
3u - 2w = 1
(e) 5x1 + 3x2 -x3 = 9
3x1 + 2x2 - x3 = 5
x1+ x2 + x3 = - 1
(f) x + z - 2w = - 3
2x - y + 2z -w = -5
-6y - 4z + 2w = 2
x + 3y + 2z - w = 1
(g) 3x1+x2 = l
x1 + 3x2 +x3 = l
x2 + 3x3 + x4 = l
x3 + 3x4 = 1