(Gm-09v – Sol) Page 2 of 11
We know we can obtain the co-factor matrix of
X
from the normal equations:
−
=
1
XX
QN
, see
the values of the elements above (NB: Symmetrical matrix, only the upper triangle is shown).
Known connections give the variance/covariance matrix:
2
0
1,373 0,227
1,222
0,288
0,659
0,256
0,474
1,739
1,012
1,420
σ
=⋅
=
XX
XX
CQ
The answers of the questions can also be found directly from the matrix above, or using the
definitions directly (on element form):
22
0
0
0,80 2,145
1,373
1,17 mm
0,80 2,717
1,32 mm
CC
DD
q
q
σσ
=
⋅
=
=
=
⋅
=
1,4 and 1,6 mm with
n - e
= 4
0
0,80 1,910 1,222
CD
q
=
⋅
=
mm
2
0
0,80 0,740
0,474
q
=
⋅
=
YY
mm
2
Interpret:
Lower standard deviation on C compared to D. Theoretically Ok, as there are 3
baselines starting or ending in point C, and only 2 in point D. The co-variances show
correlations, as expected. Large values, mainly caused by the baselines in the triangle B-C-D.
The signs are positive (+), as a positive/negative uncertainty in C also will give a
positive/negative uncertainty in D, ”they are moving in the same direction”.