i have a question regarding characteristic equation. i need help to the first question. the formula says det(A - Lambda I) = 0 my teachers solution is lamda^2 - 4 lambda + 3 = 0 so the question is how does my teacher reach that answer

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 77E
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hey bartle.

i have a question regarding characteristic equation. i need help to the first question. the formula says det(A - Lambda I) = 0 my teachers solution is lamda^2 - 4 lambda + 3 = 0 

so the question is how does my teacher reach that answer

PROBLEM 2.
Let a matrix be given by
A =
1. Find the characteristic equation.
2. Calculate, by hand, the eigenvalues and eigenvectors of A.
3. Show that the vector y =
can be written as a linear combination of A's eigen-
vectors.
PROBLEM 2. Solution
The characteristic equation is calculated as det(A – AI) = and becomes
|4 – A
0 + 1? – 4X+3 = 0.
1
Transcribed Image Text:PROBLEM 2. Let a matrix be given by A = 1. Find the characteristic equation. 2. Calculate, by hand, the eigenvalues and eigenvectors of A. 3. Show that the vector y = can be written as a linear combination of A's eigen- vectors. PROBLEM 2. Solution The characteristic equation is calculated as det(A – AI) = and becomes |4 – A 0 + 1? – 4X+3 = 0. 1
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