Question
Download Solution PDFThe eigen values of the matrix \(A = \left[ {\begin{array}{*{20}{c}} 1&1\\ { - 1}&1 \end{array}} \right]\) are
Answer (Detailed Solution Below)
1 + i, 1 - i
Detailed Solution
Download Solution PDFConcept:
Eigen values are the roots of the characteristic equation.
It is calculated by |A - λI| = 0 where λ = root or eigen value.
Calculation:
Given:
\(A = \left[ {\begin{array}{*{20}{c}} 1&1\\ { - 1}&1 \end{array}} \right]\)
The characteristic equation is, |A – λI| = 0
\(\Rightarrow \left| \begin{matrix} 1-λ & 1 \\ -1 & 1-λ \\ \end{matrix} \right|=0\)
∴ (1 - λ)2 - (-1) = 0
∴ (1 - λ)2 = -1
\(∴\left( {1 - λ } \right) = \sqrt { - 1}\Rightarrow \pm \;i\)
∴ λ = 1 + i and 1 - i
Last updated on Jun 23, 2025
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