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2 - 4 0 0 16. А — 2 3 1-1

2 - 4 0 0 16. А — 2 3 1-1

Algebra and Trigonometry (6th Edition)
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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In Exercises 15–18, find all values of λ for which det(A) = 0.

### Example 16: Matrix Representation Consider the matrix \( A \) defined as follows: \[ A = \begin{bmatrix} \lambda - 4 & 0 & 0 \\ 0 & \lambda & 2 \\ 0 & 3 & \lambda - 1 \end{bmatrix} \] Here, \(\lambda\) is a variable parameter. **Explanation of the Matrix:** - **First row**: Elements are \(\lambda - 4\), \(0\), and \(0\). - **Second row**: Elements are \(0\), \(\lambda\), and \(2\). - **Third row**: Elements are \(0\), \(3\), and \(\lambda - 1\). This matrix is a 3x3 square matrix with some elements dependent on the parameter \(\lambda\). The structure of the matrix combines zeros with the variable \(\lambda\), indicating it may be used for various calculations such as finding eigenvalues, determinants, and solving linear systems dependent on \(\lambda\). The general form and arrangement of elements within this matrix provide insight into its properties and potential applications in solving linear algebra problems.
Transcribed Image Text:### Example 16: Matrix Representation Consider the matrix \( A \) defined as follows: \[ A = \begin{bmatrix} \lambda - 4 & 0 & 0 \\ 0 & \lambda & 2 \\ 0 & 3 & \lambda - 1 \end{bmatrix} \] Here, \(\lambda\) is a variable parameter. **Explanation of the Matrix:** - **First row**: Elements are \(\lambda - 4\), \(0\), and \(0\). - **Second row**: Elements are \(0\), \(\lambda\), and \(2\). - **Third row**: Elements are \(0\), \(3\), and \(\lambda - 1\). This matrix is a 3x3 square matrix with some elements dependent on the parameter \(\lambda\). The structure of the matrix combines zeros with the variable \(\lambda\), indicating it may be used for various calculations such as finding eigenvalues, determinants, and solving linear systems dependent on \(\lambda\). The general form and arrangement of elements within this matrix provide insight into its properties and potential applications in solving linear algebra problems.
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