Home › UP Board Class 12 › mathematics › Matrices › The CHARACTERISTIC EQUATION used to find eigenva…
The CHARACTERISTIC EQUATION used to find eigenvalues of matrix A is:
A$\det(A - \lambda I) = 0$ (the classical form)
B$A \cdot \lambda = I$ (multiplication formula)
C$A^{-1} = \lambda$ (eigen-inverse)
D$\lambda = \text{tr}(A) / n$ (mean)
Answer & Solution
Correct answer: A. $\det(A - \lambda I) = 0$ (the classical form)
Eigenvalues are roots of the characteristic equation det(A − λI) = 0. The eigenvectors v satisfy Av = λv (vector unchanged in direction, scaled by λ).
Related questions
If A is a 3×3 matrix with det(A) = 5, then det(2A) isDeterminant of a 2×2 matrix [[a,b],[c,d]] equalsIf A is invertible, then A × A⁻¹ equalsA matrix with the same number of rows and columns is calledIf A is invertible 2 × 2 and A² = I then A isDeterminant of a triangular matrix equalsA square matrix A is called symmetric ifIf A and B are square matrices of same order, in general