The Eigen values of the matrix \(A = \left[ {\begin{array}{*{20}{
| The Eigen values of the matrix \(A = \left[ {\begin{array}{*{20}{c}}
0&a\\
0&0
\end{array}} \right]\)are:
A. -a, a
B. ± 1
C. ± 2
D. 0
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Right Answer is: D
SOLUTION
Concept:
For a square matrix A, an Eigenvector and Eigenvalue satisfies:
Av = λV
A = Matrix
V = Eigenvector
λ = Eigenvalue
We can write:
AV = λ IV
AV – λIV = 0
If V is non-zero, we can solve for λ by using the determinant
|A - λI| = 0
Calculation:
Given \(A\left[ {\begin{array}{*{20}{c}} 0&a\\ { 0}&{ 0} \end{array}} \right]\)
|A - λI| = 0
\(\left| {\begin{array}{*{20}{c}} { - λ }&a\\ { 0}&{ - λ } \end{array}} \right| = 0\)
(- λ) (- λ) – (0) (a) = 0
λ2 - 0 = 0
λ = 0