# Linear System of Equations with Parameters

#### 1. Solving a Linear System of Equations with Parameters by Cramer's Rule

1. Find the rank of the matrix of coefficients:

2. Find the rank of the augmented matrix:

3. Study the obtained information and determine what type of system it is:

4. Solve the compatible system by Cramer's rule (also can be solved by the Gauss Elimination method).

#### 2. Solving a Linear System of Equations with Parameters by the Gauss Elimination Method

It needs to be determined whether there is any value of * m* to make the system consistent. If so, solve the system for that value of

*.*

**m**

#### Examples

**If a = 0**.

**If a = −3**

a ≠ 1 r = 3 n = 3