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Chapter 9: Problem 2

Classify each of the following statements as either true or false. \(A 3 \times 4\) matrix has 3 rows and 4 columns.

Short Answer

Expert verified
True.

Step by step solution

01

Understand the Matrix Dimensions

A matrix is described by its dimensions, given as 'rows 脳 columns'. For example, a '3 脳 4' matrix indicates that the matrix has 3 rows and 4 columns.
02

Apply the Matrix Definition

Given a '3 脳 4' matrix, check the number of rows and columns according to the definition discussed in Step 1.
03

Conclusion

As per the definition, a '3 脳 4' matrix does indeed have 3 rows and 4 columns. Therefore, the statement is true.

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Key Concepts

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

Matrix Definition
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Each element in a matrix is known as an entry or a component. Matrices are fundamental in various fields such as mathematics, physics, engineering, and computer science.

Matrices help in representing and solving linear equations, mapping linear transformations, and performing various computational tasks. Let's start by understanding how to refer to the dimensions of a matrix, which is key to understanding matrix terminology.
Rows and Columns
To describe the size of a matrix, we use its dimensions, typically denoted as 'rows 脳 columns'. In this notation, 'rows' refers to the horizontal lines of entries, while 'columns' refer to the vertical lines.

For example, in a '3 脳 4' matrix:
* '3' specifies the number of rows
* '4' specifies the number of columns.

Each entry can be addressed using two indices: the first index denotes the row number, and the second index denotes the column number. Understanding this structure is crucial for working with matrices efficiently.
Matrix Classification
Matrices can be classified based on their dimensions and properties.

Some common types include:
  • Square Matrix: A matrix with the same number of rows and columns, e.g., a '3 脳 3' matrix.
  • Rectangular Matrix: A matrix with different numbers of rows and columns, e.g., a '2 脳 3' matrix.
  • Row Matrix: A matrix with only one row, e.g., a '1 脳 n' matrix.
  • Column Matrix: A matrix with only one column, e.g., a 'm 脳 1' matrix.
  • Diagonal Matrix: A square matrix where all non-diagonal elements are zero.
  • Identity Matrix: A diagonal matrix where all diagonal elements are one.
  • Zero Matrix: A matrix in which all elements are zero.
Classifying matrices helps in understanding their properties and determining appropriate computational methods to apply.

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Solve. $$ \left|\begin{array}{rr} {y} & {-2} \\ {4} & {3} \end{array}\right|=44 $$

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