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Chapter 8: Problem 11

Determine the order of the matrix. $$\left[\begin{array}{r}2 \\\36 \\\3\end{array}\right]$$

Short Answer

Expert verified
The order of the given matrix is 3x1.

Step by step solution

01

Identify the Columns

In the given matrix, all elements i.e. 2, 36, 3 are arranged vertically in a single line. This indicates there is only one column. This type of matrix is called a column matrix.
02

Count the Rows

Now count the number of elements vertically or the number of rows. There are three entries in the column, which means there are three rows.
03

Determine the order

As found in previous steps, there is one column and three rows. Therefore, the matrix is of order 3x1, where 3 is the number of rows and 1 is the number of columns.

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Key Concepts

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

Understanding Column Matrices
A column matrix is a type of matrix that consists of a single column of elements. You can visualize this as a vertical list of numbers arranged in one column.
This type of matrix can have any number of rows, just no more than one column.
For example, the matrix given in the exercise, \[\left[\begin{array}{c}2 \36 \3\end{array}\right]\]is a column matrix because there is only one column of numbers.
Column matrices are useful in various applications, such as in representing vectors in mathematics and physics. When working with column matrices, the significant thing to focus on is the arrangement of elements vertically in one singular column.
Counting the Number of Rows in a Matrix
The number of rows in a matrix is simply the count of horizontal lines of elements. To determine the number of rows, you look at how many horizontal slices there are in the matrix.
In the exercise provided, \[\left[\begin{array}{c}2 \36 \3\end{array}\right]\]we see there are three numbers sequentially listed.
Each number in this vertical line constitutes a separate row. Thus, there are three rows in the matrix.
  • First row: 2
  • Second row: 36
  • Third row: 3
Recognizing the number of rows is crucial as it is the first number in the order notation of a matrix, like 3x1, where "3" signifies the three rows.
Understanding the Number of Columns in a Matrix
The number of columns in a matrix indicates how many vertical lines of elements are present. A matrix can have one or more columns, depending on how the data is arranged.
In the context of our exercise, \[\left[\begin{array}{c}2 \36 \3\end{array}\right]\]there is only one vertical line of numbers, which means there is only one column in this matrix.
When describing matrices, the number of columns follows the number of rows in specifying the order. For the featured matrix, its order is 3x1, where "1" signifies the single column.
Understanding the number of columns helps in matrix manipulations and applications across various fields of study.

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Most popular questions from this chapter

Determine whether the statement is true or false. Justify your answer. When the product of two square matrices is the identity matrix, the matrices are inverses of one another.

Let \(A\) be a \(3 \times 3\) matrix such that \(|A|=5 .\) Is it possible to find \(|2 A| ?\) Explain.

Write a cryptogram for the message using the matrix \(A=\left[\begin{array}{rrr} 1 & 2 & 2 \\ 3 & 7 & 9 \\ -1 & -4 & -7 \end{array}\right]\). OPERATION OVERLOAD

Use the matrix capabilities of a graphing utility to solve (if possible) the system of linear equations. $$\left\\{\begin{array}{c}5 x-3 y+2 z=2 \\\2 x+2 y-3 z=3 \\\x-7 y+8 z=-4\end{array}\right.$$

Solve for \(x\). $$\left|\begin{array}{cc} x & 1 \\ 2 & x-2 \end{array}\right|=-1$$
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