Amila, Babu and Christy earn a total of Rs. 970 per week as the take home salary. Amila's take home salary plus twice each of the other's is Rs. 1640. Christy's take-home salary plus twice each of the other's is Rs.
1600. Using the matrices, find the take home salary of each.

Let the take-home salaries of Amila, Babu, and Christy be denoted by \( A \), \( B \), and \( C \) respectively. We are given the following system of equations based on the problem description:

1. **Total salary equation**:  
   \[
   A + B + C = 970
   \]
   
2. **Amila's salary equation**:  
   \[
   A + 2B + 2C = 1640
   \]

3. **Christy's salary equation**:  
   \[
   C + 2A + 2B = 1600
   \]

We can represent these equations in matrix form as:

\[
\begin{pmatrix}
1 & 1 & 1 \\
1 & 2 & 2 \\
2 & 2 & 1
\end{pmatrix}
\begin{pmatrix}
A \\
B \\
C
\end{pmatrix}
=
\begin{pmatrix}
970 \\
1640 \\
1600
\end{pmatrix}
\]

Let me solve this system of linear equations using matrix methods.The take-home salaries of each individual are as follows:

- Amila's salary: Rs. 300
- Babu's salary: Rs. 330
- Christy's salary: Rs. 340

Would you like a detailed explanation of how this solution was reached, or do you have any questions?

Here are 5 related questions you might consider:
1. How do you solve a system of linear equations using matrices?
2. What are other methods for solving systems of equations besides matrices?
3. How do you calculate the inverse of a matrix?
4. Can systems of linear equations always be solved using matrices?
5. What happens if the system of equations is inconsistent or dependent?

**Tip:** Always verify the consistency of your system of equations before solving, as some systems may not have a unique solution.

Amila, Babu, and Christy earn a total of Rs. 970 per week as the take-home salary. Amila's take-home salary plus twice each of the other's is Rs. 1640. Christy's take-home salary plus twice each of the other's is Rs. 1600. Using the matrices, find the take-home salary of each.

Learn how to solve a system of linear equations using matrices to find the take-home salaries of Amila, Babu, and Christy. This problem demonstrates key linear algebra concepts, such as matrix representation, system of equations, and matrix methods. Suitable for Grade 10-12 students.

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