Find the dimension of each matrix. Identify any square, column, or row matrices. [ − 6 8 0 0 4 1 9 2 3 − 5 7 1 ] \left[ \begin{matrix} -6 & 8 & 0 & 0 \\ 4 & 1 & 9 & 2 \\ 3 & -5 & 7 & 1 \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. Here we are given a matrix that appears to have three horizontal lines, each line having four elements in it. Our answer choices are a, the dimension of the matrix is three by four B. The dimension of the matrix is four by three C. The dimension of the matrix is four by one and it's a column matrix D, the dimensions of the matrix is four by four. And it is a square matrix. Recall that when we're naming the dimensions of a matrix, we say that it is the amount of rows by the amount of columns. So rows go horizontally. So I'm gonna count how many horizontal lines I have in this matrix. So I have 123. So we have three rows and then how many elements are in each row or how many hor uh vertical lines I could draw straight down. Well, tell me how many columns, 1234 columns. So we know that our matrix is, the dimensions are three by four. Is it a row matrix? Well, a row matrix only has one row. So no, it is not. Is it a column matrix? A column matrix only has one column. So this isn't it, is it a square matrix? A square matrix has the same amount of roses columns. So it is none of those special categories. So it is answer choice. A the dimensions of the matrix are three by four. Have a nice day.

7. Systems of Equations & Matrices

Introduction to Matrices

College Algebra

7. Systems of Equations & Matrices

Introduction to Matrices

2:06 minutes

Problem 9

Textbook Question

Find the dimension of each matrix. Identify any square, column, or row matrices.
$[\begin{matrix} - 6 & 8 & 0 & 0 \\ 4 & 1 & 9 & 2 \\ 3 & - 5 & 7 & 1 \end{matrix}]$

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 $m = n$, then the matrix is square.

Check if the matrix is a column matrix by seeing if it has exactly one column, i.e., if $n = 1$, then it is a column matrix.

Check if the matrix is a row matrix by seeing if it has exactly one row, i.e., if $m = 1$, then it is a row matrix.

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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. Understanding dimensions is essential for identifying matrix types and performing operations.

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 consists of a single row with multiple columns (1×n), while a column matrix has a single column with multiple rows (m×1). Recognizing these helps in understanding matrix structure and is useful in vector representation and matrix multiplication.

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