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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Using cofactor expansion down the first column, compute the determinant of A
![In this section, we explore the matrix \( A \) presented as follows:
\[ A = \begin{bmatrix}
2 & -2 & 3 \\
3 & 1 & 2 \\
1 & 3 & -1
\end{bmatrix} .\]
This matrix is a 3x3 matrix, which means it has three rows and three columns. Each entry in the matrix is defined as follows:
\[ A = \begin{bmatrix}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
a_{31} & a_{32} & a_{33}
\end{bmatrix} \]
where:
- \( a_{11} = 2 \)
- \( a_{12} = -2 \)
- \( a_{13} = 3 \)
- \( a_{21} = 3 \)
- \( a_{22} = 1 \)
- \( a_{23} = 2 \)
- \( a_{31} = 1 \)
- \( a_{32} = 3 \)
- \( a_{33} = -1 \)
Matrices are fundamental in numerous areas of mathematics and applied sciences, such as solving systems of linear equations, computer graphics, and the representation of linear transformations. Understanding how to manipulate and use matrices is essential for advancing in these fields.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9612546f-987e-4906-abd4-8f6ba2df88e4%2Fc7f03b19-b9e8-40ea-9ada-c185126d0d1e%2Ftlhd74a_processed.png&w=3840&q=75)
Transcribed Image Text:In this section, we explore the matrix \( A \) presented as follows:
\[ A = \begin{bmatrix}
2 & -2 & 3 \\
3 & 1 & 2 \\
1 & 3 & -1
\end{bmatrix} .\]
This matrix is a 3x3 matrix, which means it has three rows and three columns. Each entry in the matrix is defined as follows:
\[ A = \begin{bmatrix}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
a_{31} & a_{32} & a_{33}
\end{bmatrix} \]
where:
- \( a_{11} = 2 \)
- \( a_{12} = -2 \)
- \( a_{13} = 3 \)
- \( a_{21} = 3 \)
- \( a_{22} = 1 \)
- \( a_{23} = 2 \)
- \( a_{31} = 1 \)
- \( a_{32} = 3 \)
- \( a_{33} = -1 \)
Matrices are fundamental in numerous areas of mathematics and applied sciences, such as solving systems of linear equations, computer graphics, and the representation of linear transformations. Understanding how to manipulate and use matrices is essential for advancing in these fields.
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I cant understand what's going on. can this be explained with matrices?
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