Find the dimension of each matrix. Identify any square, column, or row matrices. [ − 9 6 2 4 1 8 ] \left[ \begin{matrix} -9 & 6 & 2 \\ 4 & 1 & 8 \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. The matrix we are given appears to have two horizontal lines of values with three values in each line. Our answer choices are a, the dimension of the matrix is three by two B. The dimension of the matrix is two by three C. The dimension of the matrix is two by one and it is a column matrix D. The dimension of the matrix is two by two and it is a square matrix. First recall when we name the dimension of a matrix that we name it as the rows by the columns. Next we call that rows go horizontally. So we're asking how many horizontal lines of values do we have? In this example, we have two horizontal lines. So we have two rows, columns run vertically or up and down. So how many columns do we have? One appears we have three. So the dimension of this matrix is two by three. It is not a row matrix as it has more than one row. It is not a column matrix as it has more than one column. And it's not a square matrix as the rows and columns are different values. So does answer choice B that the dimension of the matrix is two by three. Have a nice day.

7. Systems of Equations & Matrices

Introduction to Matrices

College Algebra

7. Systems of Equations & Matrices

Introduction to Matrices

1:44 minutes

Problem 8

Textbook Question

Find the dimension of each matrix. Identify any square, column, or row matrices.
$[\begin{matrix} - 9 & 6 & 2 \\ 4 & 1 & 8 \end{matrix}]$

Verified step by step guidance

Recall that the dimension of a matrix is given by the number of rows and columns it has, usually written as $m \times n$, where $m$ is the number of rows and $n$ is the number of columns.

To find the dimension of each matrix, count the number of horizontal entries (rows) and the number of vertical entries (columns) in the matrix.

Identify if the matrix is a square matrix by checking if the number of rows equals the number of columns, i.e., if $m = n$.

Check if the matrix is a column matrix by verifying if it has exactly one column, i.e., if $n = 1$ regardless of the number of rows.

Check if the matrix is a row matrix by verifying if it has exactly one row, i.e., if $m = 1$ regardless of the number of columns.

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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 matrix with 3 rows and 4 columns has the dimension 3×4. Knowing the dimension helps in understanding the structure and possible operations on the matrix.

Square Matrix

A square matrix has the same number of rows and columns, such as 2×2 or 5×5. This type of matrix is important because it allows for special operations like finding determinants and inverses, 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 matrices are useful in representing vectors and have unique properties in matrix multiplication and transformations.

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