Determine which of x1 X2m and X3 is an eigenvector for the m

Determine which of x_1, X_2m and X_3 is an eigenvector for the matrix A. For those that are determine the associated eigenvalue (For each vector, enter the associated eigenvalue, if it exists. If an elgenvalue does not exit, enter one.) A=[-1 0 2 3], X_1=[0 2], X_2=[1 3], X_3=[1 2] X_1 X_2 X_3

Solution

Dear Student Thank you for using Chegg Given Matrix A A = -1 2 0 3 Writing Characteristic equation for the given matrix A is A - aI=0 where I = 1 0 0 1 (-1-a)(3-a) = 0 Giving roots as a = -1,3 So Eigen values for the given matrix are -1,3 Now calculating eigen vectors a) (A+I)X = 0 0 2 x1 = 0 0 4 x2 b) (A-3I)X = 0 -4 2 x1 = 0 -4x1 + 2x2 = 0 => x1/1 = x2/2 0 0 x2 Giving the eigen vector as x= 1 2 From below 3 Eigen Vectors, x3 matches with the computed solution x1 = 0 x2 = 1 x3 = 1 2 3 2 Hence in the given question x1 1 x2 1 x3 3