https://file.aiquickdraw.com/mathbot/file/1727078416120256kgons.jpg

The image presents a vector algebra problem. It defines three vectors \( A = \begin{pmatrix} 2 \\ 3 \end{pmatrix} \), \( B = \begin{pmatrix} -1 \\ 5 \end{pmatrix} \), and \( C = \begin{pmatrix} 1 \\ 0 \end{pmatrix} \). The goal is to compute \( 2A + B - C \).

Let's proceed step by step:

1. Compute \( 2A \):
   \[
   2A = 2 \times \begin{pmatrix} 2 \\ 3 \end{pmatrix} = \begin{pmatrix} 4 \\ 6 \end{pmatrix}
   \]

2. Add \( B \) to \( 2A \):
   \[
   2A + B = \begin{pmatrix} 4 \\ 6 \end{pmatrix} + \begin{pmatrix} -1 \\ 5 \end{pmatrix} = \begin{pmatrix} 4 + (-1) \\ 6 + 5 \end{pmatrix} = \begin{pmatrix} 3 \\ 11 \end{pmatrix}
   \]

3. Subtract \( C \) from the result:
   \[
   2A + B - C = \begin{pmatrix} 3 \\ 11 \end{pmatrix} - \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 3 - 1 \\ 11 - 0 \end{pmatrix} = \begin{pmatrix} 2 \\ 11 \end{pmatrix}
   \]

Thus, the result of \( 2A + B - C \) is \( \begin{pmatrix} 2 \\ 11 \end{pmatrix} \).

Would you like any further details or clarifications? Here are 5 related questions to expand on this topic:

1. What are the properties of vector addition and scalar multiplication?
2. How do you represent vector operations geometrically?
3. Can you compute \( 3A - 2B + C \) for the same vectors \( A \), \( B \), and \( C \)?
4. How do vector operations relate to matrix operations?
5. How can you use vector operations to solve real-world problems?

**Tip:** Always keep track of the order of operations when performing vector arithmetic to avoid errors.

Jika A = (2, 3), B = (-1, 5) dan C = (1, 0), maka hasil dari 2A + B - C = .....

Learn how to solve the vector equation 2A + B - C, where A = (2, 3), B = (-1, 5), and C = (1, 0). This problem covers key concepts in vector algebra, including vector addition and scalar multiplication. Suitable for students in Grades 10-12.

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