> with(linalg):
Warning, new definition for norm
Warning, new definition for trace
> A := matrix(4,3,[1,0,0, 0,1,0, 0,0,1,1,-2,3]);

                              [1     0    0]
                              [            ]
                              [0     1    0]
                         A := [            ]
                              [0     0    1]
                              [            ]
                              [1    -2    3]

> b := vector([1,0,0,0]);
> 

                          b := [1, 0, 0, 0]

> ATA := evalm(transpose(A) &* A);

                              [ 2    -2     3]
                              [              ]
                       ATA := [-2     5    -6]
                              [              ]
                              [ 3    -6    10]

> ATb := evalm(transpose(A) &* b);

                           ATb := [1, 0, 0]

> x[p] := linsolve(ATA,ATb);

                               [14            ]
                       x[p] := [--, 2/15, -1/5]
                               [15            ]

> btilde := evalm(A &* x[p]);

                             [14                  ]
                   btilde := [--, 2/15, -1/5, 1/15]
                             [15                  ]

> ?norm
> norm(evalm(btilde - b),2);

                            1/15 sqrt(15)

> (-1/15)^2 + (2/15)^2 + (1/5)^2 + (1/15)^2;

                                 1/15

> norm(evalm(btilde-b), infinity);

                                 1/5

> norm(evalm(btilde-b), 1);

                                 7/15

>