How many rows and how many columns does this matrix have? What is its dimension? [ − 2 5 8 0 1 13 − 6 9 ] \left[ \begin{matrix} -2 & 5 & 8 & 0 \\ 1 & 13 & -6 & 9 \end{matrix} \right]

Hello, everyone. We are asked to find the number of rows and columns in the following matrix. Also to find the dimension of the matrix, we have four answer choices, all of which say slightly different numbers of rows, columns and dimensions. The first thing that's important to point out is that rows are counted horizontally. So from left to right, so to find out how many rows we have, we are going to see how many horizontal lines of digits we have, we have 123. So there are three rows in this matrix for columns, columns are counted vertically. So up and down. So we are going to see how many vertical lines we have, we have 12345. So there are five columns in this matrix recall that dimensions of a matrix are found by the number of rows by the number of columns. So we are told we have three rows and five columns. So our dimension is a three by five. So three rows, five columns, the dimension is three by five and that looks like it is answer choice B have a nice day.

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1:42 minutes

Problem 1

Textbook Question

How many rows and how many columns does this matrix have? What is its dimension?
$[\begin{matrix} - 2 & 5 & 8 & 0 \\ 1 & 13 & - 6 & 9 \end{matrix}]$

Verified step by step guidance

Identify the number of rows in the matrix by counting how many horizontal lines of elements it has. Each row is a separate horizontal group of numbers.

Identify the number of columns in the matrix by counting how many vertical lines of elements it has. Each column is a separate vertical group of numbers.

The dimension of a matrix is written as the number of rows by the number of columns, usually in the form $m \times n$, where $m$ is the number of rows and $n$ is the number of columns.

Since the matrix is given as a \$4 \times 2$ matrix, it means it has 4 rows and 2 columns.

Therefore, the dimension of the matrix is \$4 \times 2$, indicating 4 rows and 2 columns.

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Key Concepts

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

Matrix Dimensions

The dimension of a matrix is described by the number of its rows and columns, written as 'rows × columns'. For example, a 4×2 matrix has 4 rows and 2 columns. This notation helps identify the size and shape of the matrix.

Rows in a Matrix

Rows are the horizontal lines of elements in a matrix. Counting the rows tells you how many horizontal groups of numbers the matrix contains. In a 4×2 matrix, there are 4 such horizontal lines.

Columns in a Matrix

Columns are the vertical lines of elements in a matrix. Counting the columns tells you how many vertical groups of numbers the matrix contains. In a 4×2 matrix, there are 2 such vertical lines.