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Chapter 9: Problem 3

Fill in the blank. The ______ of a matrix is the number of rows and columns in the matrix.

Short Answer

Expert verified
The order of a matrix is the number of rows and columns in the matrix.

Step by step solution

01

Understand matrix dimensions

The dimensions of a matrix are defined by the number of rows and columns it contains. For instance, a matrix with 3 rows and 4 columns has dimensions 3x4.
02

Identify the term used for matrix dimensions

The term used to describe the number of rows and columns in a matrix is commonly referred to as its 'order' or 'size'. This provides a way to specify the layout of the matrix.
03

Fill in the blank

The blank in the sentence should be filled with the term that represents the number of rows and columns in a matrix, which is 'order'.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

matrix order
When we talk about the 'matrix order', we are referring to a standard way of describing a matrix. 'Order' specifies the layout by defining the number of rows and columns. If you come across a 3x4 matrix, it means the matrix has 3 rows and 4 columns. This notation is always written as rows x columns. Understanding the order helps in performing matrix operations like addition, subtraction, and multiplication, as these often require matrices of specific orders.
matrix size
The 'matrix size' essentially means the same thing as matrix order鈥攊t tells you how many rows and columns a matrix has. For example, a matrix with dimensions 2x3 has a size of 2 rows and 3 columns. Matrices can come in various sizes, and the operations you can perform on them will depend on their size. For instance, adding two matrices requires them to be of the same size, which means they must have the same number of rows and columns.
rows and columns
A matrix is made up of rows and columns. Rows are the horizontal lines of elements in a matrix, while columns are the vertical lines. The number of rows and columns in a matrix defines its shape. For example, in a 2x3 matrix, there are 2 rows and 3 columns. Each element within a matrix can be identified by its position, such as the element in the first row and second column, commonly written as (1,2). Understanding the concept of rows and columns is crucial for matrix operations and solving linear algebra problems.

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Most popular questions from this chapter

Solve each system of equations by using \(A^{-1} .\) Note that the matrix of coefficients in each system is a matrix. \(\begin{aligned} x+2 z &=-4 \\ 2 y &=6 \\ x+3 y &=7 \end{aligned}\)

Find each product if possible. $$\left[\begin{array}{rrr}1 & 1 & 0 \\\1 & 0 & 1 \\\0 & 1 & 1\end{array}\right]\left[\begin{array}{r}-2 \\\3 \\ 5\end{array}\right]$$

Solve each system, using Cramer's rule where possible. $$\begin{aligned} x+y-2 z &=1 \\ x-2 y+z &=2 \\ 2 x-y-z &=3 \end{aligned}$$

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Let \(y=-x^{4}-3 x^{3}+x^{2}-9 x+8 .\) Does \(y\) approach \(\infty\) or \(-\infty\) as \(x\) approaches \(\infty ?\)
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