Systems of Linear Equations
      Cramerís rule (using the determinant) to solve systems of linear equations
         Solving system of two equations in two unknowns using Cramer's rule
         Solving system of three equations in three unknowns using Cramer's rule
      Method of expanding a determinant of a rank n by cofactors
Cramerís rule (using the determinant) to solve systems of linear equations
Solving system of two equations in two unknowns using Cramer's rule
A system of two equations in two unknowns, the solution to a system by Cramerís rule (use of determinants).
the solution to the system  
Example:  Solve given system of linear equations using Cramerís rule.
Solution:
Solving system of three equations in three unknowns using Cramer's rule
A determinant of rank n can be evaluated by expanding to its cofactors of rank n - 1, along any row or column taking into account the scheme of the signs.   
For example, the determinant of rank n = 3,      
Example:  Solve given system of three equations in three unknowns using method of expanding to cofactors.
Solution:
Method of expanding a determinant of a rank n by cofactors, example
The value of a determinant will not change by adding multiples of any column or row to any other column or row. This way created are zero entries that simplify subsequent calculations.
Example:  An application of the method of expanding a determinant to cofactors to evaluate the determinant of the rank four.
Added is third to the second colon. Then, the second row multiplied by -3 is added to the first row. The obtained determinant is then expanded to its cofactors along the second colon:
The first colon multiplied by -1 is added to the third colon. The obtained determinant is then expanded along the third colon.
Matrices, determinants and systems of linear equations contents
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