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Here are the solutions for the given problems:

**43.**
- Correct answer: **a.**

**44.**
- Answers:
  - a. **1**
  - b. **3**
  - c. **4**

**45.**
- \( k = 2 \)

**46.**
- Correct answer: **b.**

Let me know if you'd like further details or have additional questions! 

Here are five related questions for further exploration:
1. What does it mean for a set of vectors to be linearly independent?
2. How can you determine the rank of a matrix?
3. What are the properties of a vector space in linear algebra?
4. Can you describe the difference between span and basis in vector spaces?
5. What is the significance of eigenvalues in solving systems of linear equations?

**Tip:** When solving linear systems, reducing the matrix to row echelon form simplifies the process of finding solutions.

Problems 43 to 47 in linear algebra, involving systems of linear equations, vector spaces, and matrix operations.

This page covers solving systems of linear equations, determining linear independence of vectors, and matrix operations including the inverse. It includes detailed solutions to problems related to linear combinations, spanning sets, and vector spaces.

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