🚀 go-pugleaf

Can someone please help me solve this problems.  Thanks

Consider the following system of eq. Use expansion by cofactors to
obtain the simultaneous solution

1  1  1  : -2
3  3 -1  :  6
1 -1 1   : -1

b) Obtain the inverse using Expansion by Cofactors

c) Give the solution vector

Use the Gram-Schmidt algorithm to orthoganalize the x matrix sometimes
called the design metrix then obtain the solution.  Comment on the
form X' X" .  Does this form offer any computational advantages.  e.g.
in terms of the number of steps,  number of calculations.

Y = Xb

Y                            X                                      b

11  1                -4   1   3
12  1                 3   2  -5                                   b0
10  1                 1   3  -4                                   b1
12  1                 4   4  -8                                   b2
11  1                -3   5  -2                                   b3
14  1                -1   6  -5         






Consider U below.  Show that the vectors in U are Orthogonal


        U

  1   -3   5   -1
  1   -2   0    1
  1   -1  -3    1
  1    0  -4    0
  1    1  -3   -1
  1    2   0   -1
  1    3   5    1


Comment on finding the inverse of U' U


Now suppose that Y is specified as

Y:  (5.8, 3.1, 3.2, 6.0, 7.3, 8.1, 6.2) and U is the problem above

What is the @0, @1, @2, @3, in the matrix @x read as Alpha sub zero,
alpha sub one, alpha sub two, etc.

U' Y = U' U@

Write out the four equations in algebraic form.