lisäyhtälöitä

Lisäyhtälöitä refers to augmented equations in Finnish. This concept is typically encountered in the context of linear algebra, specifically when dealing with systems of linear equations. An augmented equation or matrix is formed by combining the coefficient matrix of a system of linear equations with the constant terms on the right-hand side of the equations. This representation is particularly useful for solving systems of equations using methods such as Gaussian elimination or Gauss-Jordan elimination.

In a system of linear equations, each equation represents a relationship between variables. For example, a system of two equations with two variables, x and y, might look like:

a1*x + b1*y = c1

a2*x + b2*y = c2

The augmented matrix for this system would be:

[ a1 b1 | c1 ]

[ a2 b2 | c2 ]

The vertical line in the augmented matrix separates the coefficients of the variables from the constant terms. This format allows for a more compact and organized way to perform row operations to simplify the system and find the values of the variables. The goal of these operations is to transform the coefficient part of the augmented matrix into a reduced row echelon form, from which the solution to the system can be directly read or easily derived. The term "lisäyhtälöitä" emphasizes the "added" or "augmented" nature of the constant terms to the standard coefficient representation.