Let L be the line spanned by v_1=[1, 1, 1]. Find a basis {v_2, v_3} for the plane perpendicular to L, and verify that B= {v_1,, v_2, v_3} is a basis for R3.
Let ProjL denote the projection onto the line L. Find the matrix B for ProjL with respect to the basis B.
Can you just help me get started with the problem. I'll do the rest on my own.
We don't need eigenvectors or eigenvalues.
We need to find two vectors that span the above plane. e.g we need to find the basis for the null space of this matrix.
If it helps you can think of it as this matrix with added rows of zeros.
Since this is already in reduced row form We know that we have two free parameters. Let then
So the basis of the nullspace is
You can verify that the two above vectors are perpendicular to the first.
Can you finish from here?