Question

1.Every system of linear equations with 4 equations in 7 variables (unknowns) has infinitely many solutions.
2.Every homogeneous system of linear equations with 4 equations in 7 variables must have a 3-parameter family of solutions.
3.Every homogeneous system of linear equations with 7 equations in 7 unknowns has a unique solution.
4.No system of linear equations with 7 equations in 4 variables has a solution.
5.Every system of linear equations with 7 equations in 7 variables and whose matrix of coefficients is invertible has a unique solution.
Which is/are true?

Answer 1

1 is true (only)

Answer 2

actually it's 5

Answer 3

yes, 5 is true