Consider the following matrix.A = 23 12 −36 −19Find the eigenvalues and associated eigenvectors of A. (Arrange the eigenvalues so that 𝜆1 < 𝜆2.)𝜆1 =        with eigenvector    x1 = 𝜆2 =        with eigenvector    x2 =

Consider the following matrix.A = 23 12 −36 −19Find the eigenvalues and associated eigenvectors of A. (Arrange the eigenvalues so that 𝜆1 < 𝜆2.)𝜆1 =        with eigenvector    x1 = 𝜆2 =        with eigenvector    x2 =

a) Find the eigenvalues and the associated eigenvectors of the matrixA = [7 0 −3−9 −2 318 0 −8]

Consider the following matrix A=[−76−98] a) Find the characteristics equation of A in terms of λ (which can be typed as lambda). b) Determine the eigenvalues of A and their corresponding eigenvectors. Let λ1 and λ2 be the eigenvalues of A such that λ2>λ1, and v1 and v2 their eigenvectors respectively. So, For λ1= , we have v1= For λ2= , we have v2=

Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces) of the matrix.−1 32  − 121(a) the characteristic equationλ2−14​=0 (b) the eigenvalues (Enter your answers from smallest to largest.)(𝜆1, 𝜆2) =  −12​,12​ a basis for each of the corresponding eigenspacesx1  =  ⟨1,1⟩ x2  =  ⟨3,1⟩

To find the eigenvalues, computedet3 − λ 0 0−3 4 − λ 90 0 3 − λ = (3 − λ)(4 − λ)(3 − λ).So the eigenvalues are λ = 3 and λ = 4.We can find two linearly independent eigenvectors301 ,130 corresponding to the eigenvalue 3, and oneeigenvector010 with eigenvalue 4. The diagonalized form of the matrix is3 0 0−3 4 90 0 3 =3 1 00 3 11 0 03 0 00 3 00 0 40 0 11 0 −3−3 1 9 .Note that if you chose different eigenvectors, your matrices will be different. The middle matrix should haveentries 3, 3, 4 in some order, and you should multiply out the product to make sure you have the right answer.