Linear Algebra Answers

Find the root of the equation x^3 - x - 11 = 0 using bisection method.

up to six iterations.

Two catering firms are competing for the catering contract for the school formal

dinner. Conya Cuisine has quoted a fixed charge of K450 plus K11 per head. Fred’s

Food has quoted a fixed charge of K300 plus K12.20 per head.

i) Identify the variables and denote them with a pro-numeral.

ii) Derive the equations involving the pro-numerals.

iii) Solve the equations. What practical information is given by your solution?

iv) If 250 students are attending the dinner, which company would be cheaper?

v) How many students need to attend for the catering costs to be equal

Solve the following equations using Gauss elimination and Gauss Jordon.

2x + 7y + z = 14

x + 3y - z = 2

x + 7y + 12z = 45

use Cramer's Rule to find the solution of the systems of linear equation in terms of the parameter K.

2x - 3y = K

x + 2y = -2

use Cramer's rule to find the solution of the systems of linear equation in terms of the parameter K.

5x - Ky = 6

-2x + 2Ky = -3

Consider the following system of linear equations:

-x¹+2x²+x³=4

5x¹-2x²+3x³=-28

2x¹-x²+4x³=-23

Use Cramer’s rule to solve for x^2. (When working out determinants, indicate

with which row or column co-factor expansion is done.)

1. A worker requires 8 tanks of crude oil and petrol to get a work done. He gains 5000 

Ghana cedis per tank of crude oil used and 3000 Ghana cedis per petrol used for any 

work done. To finish the work, he further requires 10 tanks by combining 2 tanks of 

crude oil and a tank of petrol. What is the maximum profit he can make

Consider the following system of linear equations:

x − y + z = 1

x + y − 2z = 2

2x − z = 3

(a) How many solutions does the system have? Justify your

answer

Consider the following system of linear equations:

x − y + z = 1

x + y − 2z = 2

2x − z = 3

(a) How many solutions does the system have? Justify your

answer

A worker requires 8 tanks of crude oil and petrol to get a work done. He gains 5000 

Ghana cedis per tank of crude oil used and 3000 Ghana cedis per petrol used for any 

work done. To finish the work, he further requires 10 tanks by combining 2 tanks of 

crude oil and a tank of petrol. What is the maximum profit he can make?