Characteristic Roots Questions 5

In this page characteristic roots questions 5 we are going to see how to find characteristic roots of any given matrix.

Definition :

Let A be any square matrix of order n x n and I be a unit matrix of same order. Then |A-λI| is called characteristic polynomial of matrix. 

Then the equation |A-λI| = 0 is called characteristic roots of matrix.  The roots of this equation is called characteristic roots of matrix.

Another name of characteristic roots:

characteristic roots are also known as latent roots or eigenvalues of a matrix.

Question 5 :

Determine the characteristic roots of the matrix

Now we have to multiply λ with unit matrix I.

To find roots let |A-λI| = 0

 -λ(λ²-3λ²+2) = 0

λ = 0

Now we have to solve λ²-3λ²+2 to get another two values. For that let us factorize 

   λ²-3λ²+2 = 0

λ²-1λ-2λ+2 = 0

λ(λ-1)-2(λ-1) = 0

(λ-1)(λ-2) = 0

 λ - 1 = 0

 λ = 1

 λ - 2 = 0

 λ = 2

Therefore the characteristic roots (or) Eigen values are x = 0,1,2

• Equality of matrices
• Operation on matrices
• Algebraic properties of matrices
• Addition properties
• Multiplication properties
• Minor of matrix
• Determinant of matrix
• Adjoint of matrix
• Inverse of matrix
• Solving linear equation by inversion method
• Solving linear equations of two unknowns by cramer method
• Solving linear equations of three unknowns by cramer method
• Rank of matrix
• Solve linear equation of three unknowns by rank method
• Linear dependence of vector
• Characteristic Equation of Matrix
• Characteristic Vector of Matrix
• Diagonalization of Matrix
• Gauss Elimination Method
• Worksheet of matrices