Consider $R^3$(column vectors) with the standard inner product. Let L be the one dimensional subspace of $R^3$ spanned by the column vector $(2, 1, 2)^t$ .Let A be the $3 × 3$ matrix such that the linear transformation of $R^ 3$ given by $x → Ax$ is orthogonal projection onto the line L. Then the sum of the entries of A equals ___________$?$
My attempts : i take $$A = \begin{bmatrix} 1&0&0&\\0&1&0\\0&0&1\end{bmatrix}$$
now $ Ax$ =$\begin{bmatrix} 1&0&0&\\0&1&0\\0&0&1\end{bmatrix}$.$(2,1,2)^t$
IS its corrects ?????
the sum of the entries of A equals $2+1+2 =5$
Orthogonal projection matrix on the line described by the vector $v$ is $P=\dfrac{1}{\Vert v\Vert^2} vv^T$.