In a system of linear equations Ax=0, if the coefficient matrix has more columns than rows (m < n), the system must have at least one of what type of variable?
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Free variable
When a system has more variables than equations, it is considered 'underdetermined' because there isn't enough information to uniquely determine every value. This results in at least one free variable, which guarantees that the system has infinitely many solutions rather than just the trivial zero solution.
Also asked as:
- In a homogeneous system Ax=0 where there are more columns than rows, what type of variable must exist?