Service for Solving Linear Programming Problems

and other interesting typical problems
Русский

Example №1. Solving of a 2x2 System of Linear Equations by the Cramer's Rule

This solution has been made using the calculator presented on the site.
It is necessary to solve the system of linear equations using Cramer's rule.
Знак системы3x1-x2 = -14
x1 +x2 = 2
Let's write the Cramer's rule:
x1 = det A1 / det A
x2 = det A2 / det A
It is impossible to divide by zero. Therefore, if the determinant of A is zero, then it is impossible to use Cramer's rule.
Let's calculate the determinant A.   more info
The determinant A consists of the coefficients of the left side of the system.
Знак системы3x1-x2 = -14
x1 +x2 = 2
det A = 3 -1
1 1
= 3 * 1 - ( -1) * 1 = 3 + 1 = 4
The determinant A is not zero. It is possible to use the Cramer's rule.
Let's calculate the determinant A1.   more info
It is necessary to change column 1 in determinant A to the column of the right side of the system.
System det A det A1
Знак системы3x1-x2 = -14
x1 +x2 = 2
3 -1
1 1
-14 -1
2 1
det A1 = -14 -1
2 1
= -14 * 1 - ( -1) * 2 = -14 + 2 = -12
Let's calculate the determinant A2.   more info
It is necessary to change column 2 in determinant A to the column of the right side of the system.
System det A det A2
Знак системы3x1-x2 = -14
x1 +x2 = 2
3 -1
1 1
3 -14
1 2
det A2 = 3 -14
1 2
= 3 * 2 - ( -14) * 1 = 6 + 14 = 20
Result:
x1 = det A1 / det A = -12/4 = -3
x2 = det A2 / det A = 20/4 = 5








© 2010-2021

If you have any comments, please write to siteReshmat@yandex.ru