Linear Algebra Answers

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?

State Cramer’s rule. Show graphically how a system of two equations in 

two unknowns has:

(i) no solution, (ii) a unique, (iii) infinitely many solutions.

. Find the solution of the linear system using Gauss-Jordan elimination

𝑣 + 2𝑤 − 2𝑥 − 𝑦 = 0

2𝑣 + 3𝑤 − 5𝑥 + 𝑦 − 7𝑧 = 0

𝑤 + 𝑥 − 𝑦 + 𝑧 = 0

−𝑣 + 𝑤 + 5𝑥 − 𝑦 = 0