Example of Solving a System of Linear Equations by Cramer's Rule.
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It is necessary to solve the system of linear equations using Cramer's rule.
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.
|det A =||3||3|
= 3 * 2 - 3 * 1 = 6 - 3 = 3
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|
|det A1 =||9||3|
= 9 * 2 - 3 * 9 = 18 - 27 = -9
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|
|det A2 =||3||9|
= 3 * 9 - 9 * 1 = 27 - 9 = 18
x1 = det A1 / det A = -9/3 = -3
x2 = det A2 / det A = 18/3 = 6