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The question presented in the image is:

**True or False?**  
If \( c_1, c_2, c_3 \) are three columns of a \( 3 \times 3 \) matrix \( A \), and  
\[ b = 2c_1 - 3c_2 + 5c_3 \],  
then the linear system \( Ax = b \) has at least one solution.

### Explanation:

To determine if this statement is true, we need to consider the linear system \( A x = b \), where \( A \) is a matrix with columns \( c_1, c_2, c_3 \) and \( b \) is a linear combination of those columns. Specifically, \( b \) is given as a combination of the columns of \( A \):

\[ b = 2c_1 - 3c_2 + 5c_3. \]

This means that \( b \) can be expressed as a linear combination of the columns of \( A \), implying that the vector \( b \) lies within the column space of \( A \). Since \( b \) is in the column space of \( A \), the system \( A x = b \) has at least one solution (because \( b \) is reachable by some vector \( x \)).

### Conclusion:
The statement is **True**, because the vector \( b \) is a linear combination of the columns of \( A \), meaning that \( b \) is in the column space of \( A \), and thus the system has at least one solution.

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Here are five related questions:
1. How can we determine the uniqueness of the solution in such a system?
2. What is the column space of a matrix, and how does it relate to the solution of a system?
3. Can a system have more than one solution if the vector \( b \) is in the column space of \( A \)?
4. What is the difference between a homogeneous and non-homogeneous system?
5. How can we verify if a vector \( b \) lies in the column space of a matrix?

**Tip:** A matrix equation \( A x = b \) has a solution if and only if \( b \) is in the column space of \( A \).

True or False? If c1, c2, c3 are three columns of a 3x3 matrix A, and b = 2c1 - 3c2 + 5c3, then the linear system Ax = b has at least one solution.

Understand how to determine whether a linear system Ax = b has a solution by analyzing the column space of matrix A. This problem involves expressing b as a linear combination of the columns of A.

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