If a linear system has the same number of equations and variables, then it must have a unique solution.

True or false

The given statement is false.

Step-by-step explanation:

We are given the following statement:

"If a linear system has the same number of equations and variables, then it must have a unique solution."

The given statement is false because If a linear system has the same number of equations and variables, then it may have unique solution, no solution or infinitely many solution.

There could be three types of solution

no solution, unique solution and infinitely many solutions,

depending on the augmented matrix and coefficient matrix of the linear system.