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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!

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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.

The image contains four questions involving matrices, systems of equations, and linear algebra concepts like linear dependence. The tasks involve reducing matrices to row echelon form, finding matrix rank, solving systems of equations, investigating parameters for solutions, and testing vectors for linear dependence.

This exercise covers fundamental linear algebra concepts such as Gaussian elimination for matrix rank, solving systems of equations, and testing vectors for linear dependence. Suitable for undergraduate students studying linear algebra.

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