In details

Stepped Systems (continued)


II) The number of equations is less than the number of unknowns (m <n)

Example:

1st step: We nullify all coefficients of the 1st unknown from the 2nd equation:

  • We exchange the 2nd equation for the sum of the product of the 1st equation for -2 with the 2nd equation:

  • We exchange the 3rd equation for the sum of the product of the 1st equation for -1 with the 3rd equation:

2nd step: We annul the coefficients of the 2nd unknown, from the 3rd equation:

  • We exchange the 3rd equation for the sum of the product of the 2nd equation for -3 with the 3rd equation.

The system is staggered. As mdegree of indetermination (GI):

GI = n - m

To solve an undetermined system, we proceed as follows:

  • We consider the system in its staggered form:

  • We calculate the degree of indeterminacy of the system under these conditions:

GI = n-m = 4-3 = 1

As the degree of indeterminacy is 1, we assign to one of the unknowns a value supposedly known, and we solve the system for that value. Where t =, substituting this value in the 3rd equation, we get:

12z - 6= 3012z = 30 + 6
=

Known z and t, we replaced these values ​​in the 2nd equation:

Known z, t and y, we replaced these values ​​in the 1st equation:

Thus, the system solution is given by S =, with
GO.

For each value that is assigned to , we will find a quadruple solution for the system.

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