Find the dimensions of the given matrix.

*A* = 

6

−8

0

4

1

−4

 ✕ 

Identify the given entry.

*A*21 = 

Let's break down the information provided.

### Matrix \( A \):
\[
A = \begin{pmatrix}
6 \\
-8 \\
0 \\
4 \\
1 \\
-4
\end{pmatrix}
\]

### 1. Dimensions of the Matrix:
The matrix \( A \) is presented as a column matrix, meaning it has **multiple rows and one column**. By counting the rows:

- There are 6 rows.
- There is 1 column.

So, the dimensions of matrix \( A \) are **\( 6 \times 1 \)**.

### 2. Identifying the Entry \( A_{21} \):
The notation \( A_{ij} \) refers to the element in the \( i \)th row and \( j \)th column. Here, \( A_{21} \) refers to the element in the **2nd row and 1st column**.

From matrix \( A \):
\[
A = \begin{pmatrix}
6 \\
-8 \\
0 \\
4 \\
1 \\
-4
\end{pmatrix}
\]

The entry in the 2nd row and 1st column is **\(-8\)**.

### Recap:
- **Dimensions of \( A \)**: \( 6 \times 1 \)
- **Entry \( A_{21} \)**: \(-8\)

Would you like further explanations or have any other questions? Here are some related questions you might find interesting:

1. What is the entry \( A_{41} \) in matrix \( A \)?
2. How would the dimensions of \( A \) change if an additional column were added?
3. What is the general form of a column matrix?
4. How would you identify an entry in a \( 3 \times 3 \) matrix?
5. What does it mean for a matrix to be a "row vector"?

**Tip:** In a column matrix, all elements are in a single column, so identifying an entry simply involves selecting the appropriate row.

Learn how to find the dimensions of a given matrix and identify a specific entry, A21. This problem involves understanding matrix structure and notation, suitable for students in Grades 9-12.

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