In this question, you will build a matrix from the eigenvectors and eigenvalues, instead of the other way around. The matrix A has three eigenvalues : λ1=2 with eigenvector u1=(1,1,0), λ2=-3 with eigenvector u2=(1,-1,1)and λ3=12 with eigenvector u3=(1,-1,-2).
a) Normalise the eigenvectors uito give vi. Enter them in the order v1,v2,v3,where each vi has the usual format e.g. [1,2,3].
b) Recall that you can build an orthogonal matrix Pwhose columns are that set of orthonormal eigenvectors. Then (P^T)AP=D,where Dis a diagonal matrix that contains the eigenvalues along the diagonal. We now have P and D, so can find A from the formula A=PD(P^T).Enter the matrix A as a list of row vectors.