https://file.aiquickdraw.com/mathbot/file/1726548315445xj2c1khr.jpg

The matrix provided is:

\[
A = \begin{pmatrix}
-3 & 10 & 2 & 9 & -8 & 7 \\
0 & 1 & -13 & 12 & 8 & 7 \\
5 & 6 & 3 & 0 & -4 & -5
\end{pmatrix}
\]

The problem asks for the result of the following expression:

\[
a_{15} + a_{11} - a_{35} + a_{21}
\]

Where the subscripts \(a_{ij}\) refer to the element in the \(i\)-th row and \(j\)-th column of matrix \(A\).

### Step-by-Step Calculation:
1. **Locate \(a_{15}\)**: This refers to the element in the 1st row and 5th column. From the matrix, \(a_{15} = -8\).
2. **Locate \(a_{11}\)**: This refers to the element in the 1st row and 1st column. From the matrix, \(a_{11} = -3\).
3. **Locate \(a_{35}\)**: This refers to the element in the 3rd row and 5th column. From the matrix, \(a_{35} = -4\).
4. **Locate \(a_{21}\)**: This refers to the element in the 2nd row and 1st column. From the matrix, \(a_{21} = 0\).

### Expression Evaluation:

\[
a_{15} + a_{11} - a_{35} + a_{21} = (-8) + (-3) - (-4) + 0
\]

Simplifying:

\[
-8 - 3 + 4 = -7
\]

Thus, the result is \(-7\).

### Answer: 
The correct option is **C: -7**.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:
1. How do you calculate the determinant of a 3x3 matrix?
2. What is the rank of a matrix and how can you find it?
3. How do you determine if a matrix is invertible?
4. What is the significance of diagonal elements in a square matrix?
5. How can you solve a system of equations using matrix operations?

**Tip:** Remember that matrix subscripts always follow the format \(a_{ij}\), where \(i\) is the row number and \(j\) is the column number.

Diketahui matriks A = ((-3, 10, 2, 9, -8, 7), (0, 1, -13, 12, 8, 7), (5, 6, 3, 0, -4, -5)), hasil dari a15 + a11 - a35 + a21 adalah?

Learn how to calculate the result of a15 + a11 - a35 + a21 using a given 3x6 matrix. This problem involves understanding how to identify elements in a matrix and perform basic operations. Suitable for students in Grades 10-12.

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