Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Linear Algebra Inner Product Spaces, Orthonormal Basis
Let W be the column space of the matrix
\(X=\left[\begin{array}{rr}1 & -1 \\ 1 & 2 \\ 1 & -1\end{array}\right]\) then the orthogonal projection of the vector \(\left(\begin{array}{l}0 \\ 1 \\ 0\end{array}\right) \) on W is
1
\(\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right) \)
2
\(\left(\begin{array}{l}0 \\ 1 \\ 0\end{array}\right) \)
3
\(\left(\begin{array}{l}0 \\ 1 \\ 1\end{array}\right) \)
4
\(\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)\)