https://file.aiquickdraw.com/mathbot/file/17261092085725jok1qs2.jpg

The matrix given in the image is:

\[
Y = \begin{bmatrix} 
1 & -3 & 4 \\
6 & 0 & 7 \\
5 & -6 & 2 
\end{bmatrix}
\]

The question is asking for the values of specific elements in the matrix:

1. \( Y_{(3,2)} \) refers to the element in the 3rd row and 2nd column.
2. \( Y_{(2,3)} \) refers to the element in the 2nd row and 3rd column.

### Finding these values:

1. \( Y_{(3,2)} \): This is the element in the 3rd row, 2nd column, which is **-6**.
2. \( Y_{(2,3)} \): This is the element in the 2nd row, 3rd column, which is **7**.

Thus:
- \( Y_{(3,2)} = -6 \)
- \( Y_{(2,3)} = 7 \)

The correct answers for the options provided are:
- For \( Y_{(3,2)} \), the answer is **d. -6**
- For \( Y_{(2,3)} \), the answer is **a. 7**

Let me know if you'd like more details or have any other questions!

Here are 5 related questions:
1. What is the determinant of matrix \( Y \)?
2. How do you find the transpose of matrix \( Y \)?
3. What is the inverse of matrix \( Y \) (if it exists)?
4. How can you calculate the trace of matrix \( Y \)?
5. What are the eigenvalues of matrix \( Y \)?

**Tip**: Always ensure the correct indexing when working with matrices—it's row first, then column.

Identify the elements in the matrix Y = [[1, -3, 4], [6, 0, 7], [5, -6, 2]]. What are Y(3,2) and Y(2,3)?

Learn how to identify specific elements in a matrix. In this example, find Y(3,2) and Y(2,3) in the matrix Y = [[1, -3, 4], [6, 0, 7], [5, -6, 2]]. This problem covers essential matrix algebra concepts, ideal for students in Grades 9-12.

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