Homework SourseIf rightarrow v1 3 1 and rightarrow v2 5 4 are eigenvector
If rightarrow v_1 = [-3 -1] and rightarrow v_2 = [5 4] are eigenvectors of a matrix A corresponding to the eigenvalues lambda_1 = 5 and lambda_2 = 2, respectively, then A(rightarrow v_1 + rightarrow v_2) = and A(2 rightarrow v_1) = ![If rightarrow v_1 = [-3 -1] and rightarrow v_2 = [5 4] are eigenvectors of a matrix A corresponding to the eigenvalues lambda_1 = 5 and lambda_2 = 2, respectiv](/WebImages/43/if-rightarrow-v1-3-1-and-rightarrow-v2-5-4-are-eigenvector-1133841-1761606384-0.webp "If rightarrow v_1 = [-3 -1] and rightarrow v_2 = [5 4] are eigenvectors of a matrix A corresponding to the eigenvalues lambda_1 = 5 and lambda_2 = 2, respectiv")
Solution
A(v1+v2) = Av1 + Av2 = 5v1 + 2v2
= 5( -3, -1)^T + 2( 5, 4)^T
= (-5 , 3)^T
A(2v1) = 2Av1 = 2*5v1 = 10v1
= 10( -3, -1)^T
= (-30, -10)^T
