Find the 2x2 matrix A of the orthogonal projection onto the line L in R^2 that consists of all scalar multiples of the vector
(5, 1)
Remember that in general, given a linear space and a subspace with the orthogonal projection of a vector over is given by where is an orthonormal base of ( Such a base exists by Gram-Schmidt)
So in our case let this vector belongs to the line L and its norm is 1, thus ( since the dimension of the line is 1) it forms an orthonormal base of L.
Thus: from there: and note that this can be re-written as (with column vectors):