Question

Section 6.1 Eigenvalues and Eigenvectors: Problem 10 Previous Problem Problem List Next Problem 4 and the determinant is det(A) --- 45. Find the eigenvalues of A. (1 point) Suppose that the trace of a 2 x 2 matrix A is tr(A) smaller eigenvalue larger eigenvalue Note: You can earn partial credit on this problem Preview My Answers Submit Answers

Answer 1

probte m Co Trace =4 det (A) = -45 ret i and do are eigen values we know that 4,+ lg = Trace . Artda = 4 0 Also ida = det CA ) 1 lido = -45 -③ - from 0 and ② A- " = -5 la = 9 smaller eigen Value = larger eigen value =

problem 8 eigen value of A is given by (A-471 20 1-3-4 61=0 1 6 13h (+3) 6-13) – 36 co clod -39 -36 =0 Blod -75=0 (-15) Kl+5) =0 =-5,15 eigen vector ford =5 LA - 11] x = 0 noting =0 2 = 1-37

eigen vector ford=15 13 ):) =12 116A) =18] 34 - Hg 20 The smaller el genvalue (4,=-5 and Assoclated recter in The large eigen value ng = 15 and vector lg = 137