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(6) Find a 3 x 3 matrix A with eigenvectors V1 = 2 with 1 = 1, V2 = 1-1 with 1=2 and va = 1 with d = 10 T= 2 and V3 = 1 withFind a 3 × 3 matrix A with eigenvectors v1 =   1 2 3   with λ = 1, v2 =   0 −1 1   with λ = 2 and v3 =   1 1 1   with λ = 10. (Hint: A must be diagonalizable, A = P DP −1 . Figure out P and D, then compute A directly.)

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details by givun dutais. 2 -) O 10 A = 13 113 -213 -213 10 13 -13. 2 -2 10 > A= -13 513 10 -3 -413 16 -1013 4413 513 > A= A61

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