Determine whether the eigenvalues of each matrix are distinct real, repeated real, or complex -3 2 7 [4 1 -4 11 64 -120 -1 4] -69 Distinct Real ? 36 -68 ? ? >

Please solve max 20-25 minutes about chapter Linear Algebra thank u

Find all of the eigenvalues of the matrix A over the complex numbers C. Give bases for each of the corresponding eigenspaces. A = 4-1-1 = 1+i has eigenspace span has eigenspace span × !- (2-value with smaller imaginary part) (2-value with larger imaginary part)

[ 2n + 1 7][ 6 4) Determine the following matrix product, En +1 33n – 1 n + 1] 2 in terms of n. 5) Let n be a positive integer such that 7| (82-1). Prove that 7| (8-1 - 1). (Hint: Rewrite 8n*1 -1, where a portion of the expression is 8 times 8" - 1.)