Finding the QR decomposition of A, it exists because the columns of A are linearly independent. 

>	with( LinearAlgebra ): with( VectorCalculus ):

 

Warning, the names `&x`, CrossProduct and DotProduct have been rebound
 

Warning, the assigned names `<,>` and `<|>` now have a global binding
 

Warning, these protected names have been redefined and unprotected: `*`, `+`, `.`, D, Vector, diff, int, limit, series 

>	A := Matrix( [[1,1,0,1],[-1,0,1,1],[1,1,1,1]]);

 

Q is constructed from the orthnormalized columns of A using Gram Schmidt. 

>	orthonormCols := GramSchmidt( [Column( A, 1..4 )], normalized ): Q := Matrix( orthonormCols );

 

R = Q^T * A 

>	R := Transpose( Q ) . A;

 

Since A = Q * R, we should be able to regenerate the original matrix. 

>

Q . R;

 

Just for demonstration purposes, here's how to accomplish the decomposition using a native maple call. 

>	(mQ,mR) := QRDecomposition(A, fullspan); mQ . mR;

 

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