The matrix $A$ given is:

$A = \begin{pmatrix} -1 & 5 & 3 \\ \frac{1}{4} & \end{pmatrix}$

Step 1: Finding the dimensions of the matrix

• The matrix $A$ has 2 rows (first row: $-1, 5, 3$, second row: $\frac{1}{4}$).
• The matrix has 3 columns.

Thus, the dimensions of the matrix are 2 × 3 (2 rows, 3 columns).

Step 2: Identifying the entry $a_{13}$

The entry $a_{13}$ refers to the element located in the 1st row, 3rd column.

From the matrix $A$, the first row is $(-1, 5, 3)$, and the third element in this row is $3$.

So, $a_{13} = 3$.

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Would you like more details or have any questions?

Here are 5 related questions to expand on the concept:

1. What is the entry $a_{22}$ in this matrix?
2. How do you identify a specific entry in a matrix based on its indices?
3. Can a matrix have different dimensions (e.g., 3x2 or 4x1)? If so, what would that look like?
4. How do you perform matrix addition for matrices of the same dimensions?
5. How is matrix multiplication performed for matrices with compatible dimensions?

Tip: When reading a matrix entry $a_{ij}$, remember that the first subscript refers to the row number and the second refers to the column number.