Find the dimensions of the given matrix.
D = 

14	−19	

6	0
−6	3
50	19
;
 d31
4
 
Correct: Your answer is correct.
 ✕ 
2
 
Correct: Your answer is correct.
 Good work.
Identify the given entry.
d31 = 
-10
 
Incorrect: Your answer is incorrect.

To determine the dimensions of the matrix \( D \) and identify the entry \( d_{31} \), we can break down the matrix as described:

### Matrix \( D \):
\[
D = \begin{pmatrix}
14 & -19 \\
6 & 0 \\
-6 & 3 \\
50 & 19 
\end{pmatrix}
\]

### 1. Dimensions of the Matrix:
The matrix \( D \) has **4 rows** and **2 columns**. Thus, the dimensions of the matrix \( D \) are \( 4 \times 2 \).

### 2. Identifying the Entry \( d_{31} \):
The notation \( d_{ij} \) represents the entry in the \( i \)th row and \( j \)th column of the matrix. Therefore, \( d_{31} \) refers to the entry in the 3rd row and 1st column.

From the matrix \( D \):
\[
D = \begin{pmatrix}
14 & -19 \\
6 & 0 \\
-6 & 3 \\
50 & 19 
\end{pmatrix}
\]

The entry in the 3rd row and 1st column is **\(-6\)**. 

So, \( d_{31} = -6 \).

### Recap:
- **Dimensions of \( D \)**: \( 4 \times 2 \)
- **Entry \( d_{31} \)**: \(-6\)

Let me know if you need further details or explanations. Here are some related questions you might find interesting:

1. What is the entry \( d_{42} \) of the matrix \( D \)?
2. How would the dimensions change if a column was added to matrix \( D \)?
3. How do you determine the row and column number for a given entry in a matrix?
4. Can a \( 4 \times 2 \) matrix have an entry \( d_{24} \)? Why or why not?
5. How would you describe a matrix that has only one row?

**Tip:** In matrix notation \( d_{ij} \), always remember that \( i \) represents the row number and \( j \) represents the column number.

Explore how to determine the dimensions of a matrix and identify specific entries, illustrated with a detailed example. This problem involves matrix algebra, focusing on dimensions and specific entry identification.

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