# Tagged: summary

## Problem 288

In this post, we summarize theorems about the possibilities for the solution set of a system of linear equations and solve the following problems.

Determine all possibilities for the solution set of the system of linear equations described below.

(a) A homogeneous system of $3$ equations in $5$ unknowns.

(b) A homogeneous system of $5$ equations in $4$ unknowns.

(c) A system of $5$ equations in $4$ unknowns.

(d) A system of $2$ equations in $3$ unknowns that has $x_1=1, x_2=-5, x_3=0$ as a solution.

(e) A homogeneous system of $4$ equations in $4$ unknowns.

(f) A homogeneous system of $3$ equations in $4$ unknowns.

(g) A homogeneous system that has $x_1=3, x_2=-2, x_3=1$ as a solution.

(h) A homogeneous system of $5$ equations in $3$ unknowns and the rank of the system is $3$.

(i) A system of $3$ equations in $2$ unknowns and the rank of the system is $2$.

(j) A homogeneous system of $4$ equations in $3$ unknowns and the rank of the system is $2$.