For matrix C, find the associated eigenvalues. c=[-5₁ 3 C -1 O1 and 5 O4 and 3 O-5 and 2 O4 and 6

The matrix (image attached) has three distinct real eigenvalues if and only if   Fill in blank < k < Fill in blank

3. Find the Eigen value of the following matrix: (3 1 1) B = (2 4 2 \1 1 3/

Let A be a symmetric matrix with eigenvalues 3 and 0 and corresponding eigenvectors (a, b) and (c, d). a If the eigenvector matrix is S= then the eigenvectors of B = S-1 A S are O a. (1, 0), (0, 1) O b. (3, 3), (-3, -3) Oc. cannot be determined O d. (2, ), (-2. -i) O e. (2, 2), (-2, -2)

For the matrix A, find (if possible) a nonsingular matrix P such that P1AP is diagonal. (If not possible, enter IMPOSSIBLE.) 100 15-1 L-30 5. A= 41 p-¹AP = Verify that PAP is a diagonal matrix with the eigenvalues on the main diagonal. 2 000 000 11

Let A be 2 x 2 matrix. if trace A =8 and det(A)= 12 then the eigenvalues of A are: Select one: a. 3,4 b. 4,4 C. 2,6 d. 10,2

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