Question

How do you determine the line of possible solutions to an underdetermined system of linear equations?

Answer 1

Hint: In the given question, we are required to determine the line of possible solutions to an underdetermined system of linear equations. So, in case of linear equations, we need to have the same number of equations as the number of variables in order to find the solution or the values of the variables.

Complete step by step answer:
Try to think about when we are given a number of unknown variables. In such a case, how many linear equations are required relating them with each other in order to find the values of those unknown variables i.e., we can find the value of as many linear equations relating those variables are available to us or given to us in the problem itself.
If we are given more variables and less equations, the number of values of the unknown variables we would be able to find is the number of equations given to us. One must have an independent equation for each variable to be able to calculate a solution.
Underdetermined systems may have an infinite number of possible solutions - it all depends on the relationships of those extra variables.

Note: An underdetermined system of linear equations describes hyperplane (or possibly a plane or a line.) You have \[45\] variables and \[5\] equations. Given any arbitrary values for the last \[40\] variables, exact values of the first \[5\] can be calculated. The set of all positive solutions could only be described by boundary equations. In mathematics, one must have as many independent as many linear equations relating those variables in order to find the values of variables.