https://file.aiquickdraw.com/mathbot/file/1727311998560lgvmpg85.jpg

The problem given in the image involves matrices and the task is to calculate the expression \( 2A + B + 3C \), where matrices \( A \), \( B \), and \( C \) are defined as follows:

\[
A = \begin{pmatrix} 4 & -4 \\ 2 & 1 \end{pmatrix}, \quad B = \begin{pmatrix} -3 & -2 \\ -1 & 5 \end{pmatrix}, \quad C = \begin{pmatrix} 5 & 4 \\ -2 & -1 \end{pmatrix}
\]

We need to compute:

\[
2A + B + 3C
\]

Let's break it down step-by-step:

1. First, calculate \( 2A \) by multiplying matrix \( A \) by 2.
2. Then calculate \( 3C \) by multiplying matrix \( C \) by 3.
3. Add the resulting matrices together along with matrix \( B \).

I'll perform these calculations now.The result of the matrix operation \( 2A + B + 3C \) is:

\[
\begin{pmatrix} 20 & 2 \\ -3 & 4 \end{pmatrix}
\]

Would you like further details on any specific step or another explanation? 

Here are 5 related questions to extend the learning:
1. How do you multiply a scalar with a matrix?
2. What are the properties of matrix addition?
3. Can matrix multiplication be applied here? If so, how would the result differ?
4. How would you calculate the determinant of the resulting matrix?
5. What happens if you transpose the result of \( 2A + B + 3C \)?

**Tip**: Always ensure that the dimensions of matrices are the same when performing matrix addition or subtraction.

Diketahui matriks A = \begin{pmatrix} 4 & -4 \\ 2 & 1 \end{pmatrix}, B = \begin{pmatrix} -3 & -2 \\ -1 & 5 \end{pmatrix}, dan C = \begin{pmatrix} 5 & 4 \\ -2 & -1 \end{pmatrix}, nilai 2A + B + 3C adalah ...

Solve the matrix operation 2A + B + 3C where matrices A, B, and C are provided. This solution demonstrates key concepts of matrix addition and scalar multiplication, with step-by-step guidance for high school students (Grades 10-12).

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