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Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 5 - Systems and MatricesProblem 1
Chapter 6, Problem 1

How many rows and how many columns does this matrix have? What is its dimension?
[−2580113−69]\(\left\)[ \(\begin{matrix}\) -2 & 5 & 8 & 0 \\ 1 & 13 & -6 & 9 \(\end{matrix}\) \(\right\)]

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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.
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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.
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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.
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Related Practice
Textbook Question

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Textbook Question

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Textbook Question

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Textbook Question

Answer each question. What is the product of [64−18]\(\left\)[ \(\begin{matrix}\) 6 & 4 \\ -1 & 8 \(\end{matrix}\) \(\right\)] and I2 (in either order)?

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Textbook Question

Fill in the blank(s) to correctly complete each sentence. For the following statement to be true, the value of x must be ____, and the value of y must be ____.

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Textbook Question

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