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(Solved): Please show all work in finding the vectors. C: An example of diagonalisation : Let T be the operat ...
Please show all work in finding the vectors.
C: An example of diagonalisation : Let T be the operator of C3 with matrix M=⎝⎛1002i01+i2i−1−i⎠⎞ 1) Find 3 vectors e1e2e3 satisfying the equations : ⎩⎨⎧T(e1)=e1T(e2)=ie2T(e3=−ie3 2) Find the matrix of T in the basis (e1,e2,e3). 3) Use this to find T4 with as little computation as possible.
Now we can see that given matrix M is a upper triangular matrix so its diagonal elements 1,i,-i are its eigenvalues. 1)Now where is identity matrix. Now writing this system in augmented matrix we get Now we find row reduced echelon formMultiply each element of by to make the entry at a . Perform the row operation Multiply each element of by