1) 2) 3) 01 0 a. Find the characteristic polynomial of the matrix A = 1 D 0 1 0 O [Hint: Use a cofactor expansion or a shortcut formula for the determinant] b. Give the only (real) eigenvalue of A and nd its corresponding eigenspace. c. Describe what the linear transformation T (55) = A}? does in geometric terms. [Hintz Where do the axes go?] What is the geometric signicance of the eigenspace in part b.? 0 3 1 The characteristic polynomial of A = 1 2 1 is 4.3 + 2&2 A. Find the 3 9 4 eigenvalues of A, and for each eigenvalue nd a basis for its corresponding eigenspace. 71 32 each eigenvalue. [Hint They are irrational numbers] Give all answers both in exact form and as decimal approximation. Find the eigenvalues of A = and one corresponding eigenvector for