• Linear Systems
• Gauss
• Cramer's Rule
• Solving
• Homogeneous
• 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

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