## The Possibilities For the Number of Solutions of Systems of Linear Equations that Have More Equations than Unknowns

## Problem 295

Determine all possibilities for the number of solutions of each of the system of linear equations described below.

**(a)** A system of $5$ equations in $3$ unknowns and it has $x_1=0, x_2=-3, x_3=1$ as a solution.

**(b)** A homogeneous system of $5$ equations in $4$ unknowns and the rank of the system is $4$.

(*The Ohio State University, Linear Algebra Midterm Exam Problem*)

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