Obtain the eigen values of the matrix [ 1 2 34 49 ] A = [ 0 2 43 94 ] [ 0 0 -2 104 ] [ 0 0 0 -1 ]

GATE 2002 · Engineering Mathematics · Eigen Value · medium

Answer: Eigenvalues are 1, 2, -2, -1

1. Identify the triangular structure: Matrix A has zeros below the diagonal (a_{21}=0, a_{31}=0, a_{32}=0, a_{41}=a_{42}=a_{43}=0). Therefore A is upper triangular.
2. Read off eigenvalues from diagonal: lambda_1 = a_{11} = 1, lambda_2 = a_{22} = 2, lambda_3 = a_{33} = -2, lambda_4 = a_{44} = -1.