1. The problem statement, all variables and given/known data Define L:R3-->R3 by L(x,y,z)=(y-z,x+z,-x+y). A. Show that L is self-adjoint using the standard orthonormal basis B of R3. B. Diagonalize L and find and orthogonal basis B of R3 of eigenvectors of L and the diagonal matrix. C. Considering only the eigenvalues of L, determine if L is an isomorphism. D. Find L(1,0,0) using the diagonal matrix of L. 2. Relevant equations L(x,y,z)=(y-z,x+z,-x+y) Matrix of L with respect to orthonormal basis: 0 1 -1 1 0 1 -1 1 0 Diagonal matrix of L: 1 0 0 0 1 0 0 0 -2 3. The attempt at a solution I already answered A and B. For C, I said L is not an isomorphism because of repeated eigenvalues. For D, I am not sure how to find the linear transformation using only the diagonal matrix, but I know the answer is (0,1,-1).