Projection Matrix - Maple Programming Help

Projection Matrix

 Description Generate a projection matrix that will project a vector onto the subspace spanned by a list of vectors.

Enter a list of vectors.

 > $\left[{[}\begin{array}{c}{3}\\ {0}\\ {1}\\ {2}\end{array}{]}{,}{[}\begin{array}{c}{2}\\ {-}{1}\\ {0}\\ {1}\end{array}{]}{,}{[}\begin{array}{c}{-}{4}\\ {1}\\ {2}\\ {3}\end{array}{]}\right]$
 $\left[\left[\begin{array}{r}{3}\\ {0}\\ {1}\\ {2}\end{array}\right]{,}\left[\begin{array}{r}{2}\\ {-}{1}\\ {0}\\ {1}\end{array}\right]{,}\left[\begin{array}{r}{-}{4}\\ {1}\\ {2}\\ {3}\end{array}\right]\right]$ (1)

Calculate the Projection Matrix.

 > $\mathrm{LinearAlgebra}\left[\mathrm{ProjectionMatrix}\right]\left(\right)$
 $\left[\begin{array}{cccc}{1}& {0}& {0}& {0}\\ {0}& \frac{{5}}{{6}}& \frac{{1}}{{3}}& {-}\frac{{1}}{{6}}\\ {0}& \frac{{1}}{{3}}& \frac{{1}}{{3}}& \frac{{1}}{{3}}\\ {0}& {-}\frac{{1}}{{6}}& \frac{{1}}{{3}}& \frac{{5}}{{6}}\end{array}\right]$ (2)
 Commands Used