The image contains four questions involving matrices, systems of equations, and linear algebra concepts like linear dependence. Here's an outline of how we can tackle these:

1. Matrix Row Echelon Form and Rank:

• You are required to reduce three matrices to their row echelon form and determine their rank. To solve this:
  • Use Gaussian elimination to transform each matrix into its row echelon form.
  • The number of non-zero rows will give the rank of the matrix.

2. Consistency of Systems of Equations:

• The three systems of linear equations need to be tested for consistency, and if consistent, the solutions must be found.
  • Apply methods like substitution, elimination, or matrix methods (such as augmented matrices and Gaussian elimination) to solve.

3. Investigation of Values of Parameters for Solutions:

• For part (a) and (c), you are asked to determine the values of parameters $\lambda$ and $\mu$ that give no solutions, unique solutions, or infinite solutions.
• For part (b), you need to determine for which value of $k$ the system has infinite solutions.
• This typically involves analyzing the determinant and the rank of the coefficient matrix for conditions of consistency.

4. Testing for Linear Dependence of Vectors:

• For each set of vectors, you are to check for linear dependence and, if they are dependent, find the relations between them.
• This involves checking if one vector can be written as a linear combination of others, which can be done by forming a matrix with the vectors as columns and reducing it to row echelon form.

Would you like detailed solutions for a specific part of the problem? Let me know which question you'd like to begin with!

Here are 5 follow-up questions:

1. Would you like to see step-by-step Gaussian elimination for any of the matrices in Question 1?
2. Do you need help solving a specific system of equations from Question 2?
3. Should I walk you through how to investigate the values of $\lambda$ and $\mu$ in Question 3?
4. Would you like to verify if one of the vector sets from Question 4 is linearly dependent?
5. Do you need clarification on how to find the rank of a matrix?

Tip: When solving systems of linear equations, always verify if the determinant of the coefficient matrix is zero. If it's zero, the system may either have no solution or infinite solutions.