Find the dimension of each matrix. Identify any square, column, or row matrices. [ 8 − 2 4 6 3 ] \left[ \begin{matrix} 8 & -2 & 4 & 6 & 3 \end{matrix} \right]

Hello, everyone. We are asked to find the dimension of the matrix and categorize the matrix as a row column or square matrix. So the matrix we are given has one single line of numbers 35 negative 712. Our answer choices are a, the dimension of the matrix is one by four and it's a row matrix B, the dimension of the matrix is four by one and it is a column matrix C, the dimension of the matrix is a five by one and it is a column matrix D. The dimension of the matrix is a one by five and it is a row matrix. The first thing to recall is then when we name matrices, we name them as the amount of rows by the amount of columns looking at what we're given here. I recall that rows go horizontally and columns go vertically. So horizontally we only have one single row. So we know that the first numbers are one. How many columns are there? Well, there's how many numbers going down? 12345. So there are five columns because we could have five vertical lines drawn straight down through our values. Next thinking about row column and square matrices, row matrices are called such because they only have a single row. And that's what we have. In this case, we have one single row. So this means that answer choice D is correct that the dimension of the matrix is a one by five. And that it's a row matrix have a nice day.

7. Systems of Equations & Matrices

Introduction to Matrices

College Algebra

7. Systems of Equations & Matrices

Introduction to Matrices

2:04 minutes

Problem 10

Textbook Question

Find the dimension of each matrix. Identify any square, column, or row matrices.
$[\begin{matrix} 8 & - 2 & 4 & 6 & 3 \end{matrix}]$

Verified step by step guidance

Understand that the dimension of a matrix is given by the number of rows multiplied by the number of columns, written as $m \times n$, where $m$ is the number of rows and $n$ is the number of columns.

Given the matrix is described as a $5 \times 1$ matrix, this means it has 5 rows and 1 column.

Write down the dimension explicitly as $5 \times 1$.

Identify the type of matrix based on its dimensions: since it has only one column, it is a column matrix.

Note that it is not a square matrix because the number of rows (5) is not equal to the number of columns (1), and it is not a row matrix because it has more than one row.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Matrix Dimension

The dimension of a matrix is described by the number of its rows and columns, written as 'rows × columns'. For example, a 5×1 matrix has 5 rows and 1 column. Understanding dimensions helps in identifying the size and structure of the matrix.

Square Matrix

A square matrix has the same number of rows and columns (n×n). This property is important because square matrices have unique characteristics, such as the possibility of having a determinant and an inverse, which are not defined for non-square matrices.

Row and Column Matrices

A row matrix has only one row and multiple columns (1×n), while a column matrix has one column and multiple rows (m×1). These special forms are useful in vector representation and simplify certain matrix operations.

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