Question

-3 221 Let A-4 3 2. You are given that 1 is an eigenvalue of A. What is the algebraic mutiplicity of 17 2 -1 2 Answer Check

Answer 1

since the Eugen value $\lambda=1$ is repeated twice. So the algebric multiplicity of $\lambda=1$ is 2.

Let A = [-3 2 -2 -4 3 -2 2 -1 2] since lambda = 1 is the one eigen value of A let lambda_2 and lambda_3 be the another two eigne vectors of A. Then sum of the eigen values of A is equal to trace of A that is 1 + lambda_2 + lambda_3 = -3 + 3 + 2 1 + lambda_2 + lambda_3 = 2 lambda_2 + lambda_3 = 1 and the product of the eigen values of A is equal to the determinant of A. Then 1.lambda_2.lambda_3 = 0 since det(A) = 0 so, one of the lambda_2 or lambda_3 is zero and the remaining eigen value is 1 so,the eigen values of A are lambda = 1,1,0.