Math Problem Statement
Find the dimensions of the given matrix.
A =
6
−8
0
4
1
−4
✕
Identify the given entry.
A21 =
Solution
Let's break down the information provided.
Matrix :
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.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Operations
Matrix Dimensions
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12