Question

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

True or false

Answer 1

The given statement is false.

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.