I found a very odd thing.
A matrix multiplied by its inverse matrix should be an
identity matrix.
But why the following thing happens?
<a%*%solve(a) is not an identity matrix>
> x%*%t(x)
[,1] [,2] [,3] [,4] [,5]
[1,] 108.16 58.24 32.24 66.56 225.68
[2,] 58.24 31.36 17.36 35.84 121.52
[3,] 32.24 17.36 9.61 19.84 67.27
[4,] 66.56 35.84 19.84 40.96 138.88
[5,] 225.68 121.52 67.27 138.88 470.89
> a=x%*%t(x)
> solve(a)
[,1] [,2] [,3]
[,4] [,5]
[1,] -1.372649e+14 1.078492e+14 -2.553747e+14
1.126842e+14 4.120191e+13
[2,] -1.174558e+14 1.543860e+14 2.323143e+14
-1.375074e+14 2.381809e+13
[3,] -3.062129e+14 6.914056e+14 -1.656744e+15
7.007732e+14 -1.672741e+12
[4,] 1.761208e+14 -3.724017e+14 7.773835e+14
-2.156631e+14 -3.575351e+13
[5,] 8.789836e+13 -8.046912e+13 6.984285e+13
-5.502429e+13 -1.510937e+13
> a%*%solve(a)
[,1] [,2] [,3] [,4]
[,5]
[1,] 2.0410156 1.4433594 -4.169922 0.4003906
1.2170410
[2,] -2.5146484 1.9208984 -1.84912w=1 1.1879883
1.1203613
[3,] -1.5356445 -0.8549805 -1.008789 0.4116211
0.6218872
[4,] -0.5898438 -0.2539063 3.592773 2.0351563
0.7849121
[5,] 1.5000000 -1.1289063 -2.070313 -0.4003906
2.1386719
>