(a) (i) Show that (x, y, z) = (t + 2, −2t − 1, t) is a general solution of the system
2x + 4y + 6z = 0
4x + 5y + 6z = 3
7x + 8y + 9z = 6.
(ii) Solve the following system
x1 − x2 + 4x5 = 2
x3 − x5 = 2
x4 − x5 = 3.
(b) Solve the following system by Gauss-Jordan elimination:
2x + 8y + 4z = 2
2x + 5y + z = 5
4x + 10y − z = 1.
(c) Solve the system in 1(b) by using Cramer’s rule. First, discuss the applicability of Cramer’s rule to the system.
If Mary's iphone charger is 6 1/2 feet long and her bed is 9 feet from the outlet in the wall, how much longer would her charger need to be for her to be able to charge her phone in bed?
Find the total number of seats of an amphitheater if it has 70 rows with 40 seats, 44 seats and 48 seats on the first, second and third rows respectively.