https://file.aiquickdraw.com/mathbot/file/1726659554570xofcpvkd.jpg

The image shows a matrix with four rows and four columns, with the notation \( i = 1 \) and \( j = 4 \). This likely indicates that you are required to perform a specific operation or retrieve a specific element from the matrix based on the indices \( i \) and \( j \).

### Matrix:
\[
\begin{pmatrix}
1 & 8 & 2 & -3 \\
3 & -2 & 0 & 4 \\
5 & -3 & 7 & -1 \\
3 & 2 & 0 & 2
\end{pmatrix}
\]

### For \( i = 1 \) and \( j = 4 \):
- \( i \) refers to the row number.
- \( j \) refers to the column number.

So, you are looking for the element at the intersection of the 1st row and the 4th column, which is \(-3\).

Thus, the element at \( (i = 1, j = 4) \) is \( -3 \).

Would you like further details or additional questions related to this topic? Here are five possible follow-up questions:

1. How would you calculate the determinant of this 4x4 matrix?
2. What is the minor of the element located at \( (i = 1, j = 4) \)?
3. How can we find the cofactor of the element at \( (i = 1, j = 4) \)?
4. What is the inverse of this matrix, if it exists?
5. How do you perform Gaussian elimination on this matrix?

### Tip:
To calculate the determinant of a 4x4 matrix, you can use cofactor expansion along any row or column for simplicity.

Given the 4x4 matrix, what is the element located at (i = 1, j = 4)?

Learn how to locate the element at the intersection of the 1st row and 4th column in a 4x4 matrix. This problem covers fundamental concepts in linear algebra, including matrix indexing and identification. Suitable for students in Grades 9-12.

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