Find the eigenvalues of A, given that A =and its eigenvectors are V₁ =The eigenvalues areand1-1142612]78-6 -9V₂ =-1and V3 =0B

To find the eigenvalues of A, given that A=1612-4782-6-9and its eigenvectors are v1=11-1, v2=-1-21,…

Answered: Find the eigenvalues of A, given that A…

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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Find the eigenvalues of A, given that A =
and its eigenvectors are V₁ =
The eigenvalues are
and
1
-1
1
4
2
6
12]
7
8
-6 -9
V₂ =
-1
and V3 =
0
B

Expert Solution

Step 1

$To find the eigenvalues of A, given that A = [\begin{matrix} 1 & 6 & 12 \\ - 4 & 7 & 8 \\ 2 & - 6 & - 9 \end{matrix}] and its eigenvectors are v_{1} = [\begin{matrix} 1 \\ 1 \\ - 1 \end{matrix}], v_{2} = [\begin{matrix} - 1 \\ - 2 \\ 1 \end{matrix}], and v_{3} = [\begin{matrix} 0 \\ - 2 \\ 1 \end{matrix}] .$