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The problem provided asks to calculate the matrix expression \( A \times B + C \), where the matrices \( A \), \( B \), and \( C \) are:

\[
A = \begin{pmatrix} 4 & -3 \\ 5 & 2 \end{pmatrix}, \quad B = \begin{pmatrix} 10 & -2 \\ 4 & 6 \end{pmatrix}, \quad C = \begin{pmatrix} 7 & -5 \\ 1 & 3 \end{pmatrix}
\]

### Step 1: Matrix Multiplication \( A \times B \)

To multiply two matrices, we use the rule:
\[
(A \times B)_{ij} = \sum_{k} A_{ik} B_{kj}
\]
For \( A \times B \):

\[
A \times B = \begin{pmatrix} 4 & -3 \\ 5 & 2 \end{pmatrix} \times \begin{pmatrix} 10 & -2 \\ 4 & 6 \end{pmatrix}
\]

- First row, first column: \( (4 \times 10) + (-3 \times 4) = 40 - 12 = 28 \)
- First row, second column: \( (4 \times -2) + (-3 \times 6) = -8 - 18 = -26 \)
- Second row, first column: \( (5 \times 10) + (2 \times 4) = 50 + 8 = 58 \)
- Second row, second column: \( (5 \times -2) + (2 \times 6) = -10 + 12 = 2 \)

Thus, the result of \( A \times B \) is:
\[
A \times B = \begin{pmatrix} 28 & -26 \\ 58 & 2 \end{pmatrix}
\]

### Step 2: Matrix Addition \( (A \times B) + C \)

Now, add matrix \( C \) to \( A \times B \):

\[
\begin{pmatrix} 28 & -26 \\ 58 & 2 \end{pmatrix} + \begin{pmatrix} 7 & -5 \\ 1 & 3 \end{pmatrix}
\]

- First row, first column: \( 28 + 7 = 35 \)
- First row, second column: \( -26 + (-5) = -31 \)
- Second row, first column: \( 58 + 1 = 59 \)
- Second row, second column: \( 2 + 3 = 5 \)

Thus, the result is:
\[
A \times B + C = \begin{pmatrix} 35 & -31 \\ 59 & 5 \end{pmatrix}
\]

Would you like further clarification on any step or more details?

Here are some related questions for practice:
1. How do you multiply two 3x3 matrices?
2. What are the conditions for matrix multiplication to be possible?
3. How do you compute the determinant of a 2x2 matrix?
4. What properties do matrix addition and multiplication share?
5. How can you solve a system of linear equations using matrices?

**Tip:** Always check matrix dimensions before performing operations to ensure they are compatible!

Diketahui matriks A = (4, -3; 5, 2), B = (10, -2; 4, 6), dan C = (7, -5; 1, 3), maka A × B + C = ...

Learn how to calculate the matrix expression A × B + C where A, B, and C are 2x2 matrices. This solution involves matrix multiplication and addition, including step-by-step calculations for each operation. Suitable for students in Grades 10-12.

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