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It appears you've uploaded a PDF containing your **MATH1003 Linear Algebra 1 Assignment 2**. Here’s a brief overview of the problems included in the assignment:

1. **System of Equations**:
   - Part (a): Solve a system of three equations using **Gauss-Jordan reduction**.
   - Part (b): Solve another system of equations (with four variables) using the same method.

2. **Special Cases of a System**:
   - You are asked to find conditions on constants **k** and **h** for the system to have:
     - No solution.
     - A unique solution.
     - Infinitely many solutions.

3. **Augmented Matrix**:
   - Given a system with an augmented matrix, find values of **a** and **b** such that:
     - The system has infinitely many solutions.
     - The system is inconsistent.

4. **Solving 2x2 Systems**:
   - Solve two 2x2 linear systems using **reduced row echelon form** by incorporating the right-hand side into a matrix.

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Would you like to start with any specific problem, or would you like a step-by-step guide for solving one of these problems?

### 5 Follow-up Questions:
1. Do you need help with Gauss-Jordan elimination?
2. Would you like to discuss the conditions for solutions of systems based on matrix rank?
3. Do you want an example of finding a unique solution vs. infinitely many solutions?
4. Are you familiar with how to interpret augmented matrices and their consistency?
5. Do you need further explanation on computing the reduced row echelon form (RREF)?

**Tip**: When solving systems of linear equations, always check the rank of the coefficient matrix and augmented matrix to determine consistency and the number of solutions.

Solve a system of equations using Gauss-Jordan reduction and investigate special cases of a system for unique, no, or infinite solutions.

Explore the use of Gauss-Jordan reduction to solve linear systems of equations, with conditions for no, unique, or infinitely many solutions. Learn how matrix augmentation and reduced row echelon form (RREF) help in analyzing these cases, suitable for first-year university students.

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