Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
Compute the determinant of A using the cofactor expansion across the second row, where
![In the context of matrix algebra, consider the following matrix:
\[ A = \begin{pmatrix}
2 & -2 & 3 \\
3 & 1 & 2 \\
1 & 3 & -1
\end{pmatrix} \]
This matrix \(A\) is a 3x3 matrix, meaning it has three rows and three columns.
To break down each element of the matrix:
- The element in the first row and first column is 2.
- The element in the first row and second column is -2.
- The element in the first row and third column is 3.
- The element in the second row and first column is 3.
- The element in the second row and second column is 1.
- The element in the second row and third column is 2.
- The element in the third row and first column is 1.
- The element in the third row and second column is 3.
- The element in the third row and third column is -1.
Each row of the matrix can represent different data points or coefficients depending on the context of the problem it is used to solve. For example, this matrix could be part of a set of equations in linear algebra, where each row represents a linear equation.
Understanding how to manipulate and utilize matrices is fundamental in fields such as computer graphics, engineering, and applied mathematics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad281aeb-79af-4eda-b9b4-346ba477171b%2Fd518d673-bdad-4263-a54b-166f9d6fd755%2Fi9xr6qm_processed.png&w=3840&q=75)
Transcribed Image Text:In the context of matrix algebra, consider the following matrix:
\[ A = \begin{pmatrix}
2 & -2 & 3 \\
3 & 1 & 2 \\
1 & 3 & -1
\end{pmatrix} \]
This matrix \(A\) is a 3x3 matrix, meaning it has three rows and three columns.
To break down each element of the matrix:
- The element in the first row and first column is 2.
- The element in the first row and second column is -2.
- The element in the first row and third column is 3.
- The element in the second row and first column is 3.
- The element in the second row and second column is 1.
- The element in the second row and third column is 2.
- The element in the third row and first column is 1.
- The element in the third row and second column is 3.
- The element in the third row and third column is -1.
Each row of the matrix can represent different data points or coefficients depending on the context of the problem it is used to solve. For example, this matrix could be part of a set of equations in linear algebra, where each row represents a linear equation.
Understanding how to manipulate and utilize matrices is fundamental in fields such as computer graphics, engineering, and applied mathematics.
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