The uploaded image contains a set of mathematical problems involving matrices and systems of equations. It includes questions on:

1. Finding the ranks of matrices by reducing them to echelon form.
2. Determining ranks by reducing matrices to normal form.
3. Solving systems of linear equations.
4. Investigating the conditions for the existence of solutions for systems of equations.

Would you like assistance solving a specific problem from the image, or would you prefer an overview of the steps to approach these types of questions? Let me know which problem you'd like to focus on!

Here are some follow-up questions that could help guide further discussion:

1. Do you need a detailed solution for finding the rank of a matrix?
2. Would you like help with understanding how to solve systems of equations using matrix methods?
3. Do you need clarification on the difference between echelon form and normal form of matrices?
4. How would you approach solving a system of equations with infinite solutions?
5. Are you interested in methods to determine if a system of equations has no solution?

Tip: When solving for the rank of a matrix, always ensure the matrix is in a consistent echelon form for accurate results.