(adsbygoogle = window.adsbygoogle || []).push({}); 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).

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# Find linear transformation using diagonal matrix

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