This is more for part C and D. For part c I think we gotta use gram schmidt. But how do we apply it? Thanks

3. Consider the linear transformation 7: R3 - R* defined by T(X1, 12, 13) = (511 -212 + 4x3, -2x1 + 812 + 2x3, 4x1 + 2r2 + 513), (11, 12, 13) ER. (a) Find the matrix A = [T] representing 7 with respect to standard coordinates. (b) Find the characteristic polynomial and eigenvalues of A. For each eigenvalue, find it algebraic multiplicity. (c) Determine if A is orthogonally diagonalizable. If it is, find an orthonormal basis for consisting only of eigenvectors of A. (d) Find an orthogonal matrix P and a diagonal matrix D so that A = PDPT