x1=matrix(c(1,1,1,1,1,1,0,-1,0,1,-1,-1,-1,0,1,0,-1,1,-1,0,0,1,-1,0),nrow=6)

x2=x1
x2[5,]=c(1,-1,0,-1)
x2[6,]=c(1,1,0,0)

x3=matrix(c(
1,1,0,1,
1,-1,0,-1,
1,1,0,1,
1,-1,0,0,
1,1,0,0,
1,-1,0,0
),byrow=T,nrow=6)

x4=x3
x4[,4]=c(1,-1,0,0,0,0)

x5=x4
x5[2,4]=0

x6=x5
x6[,4]=c(1,-1,1,-1,1,0)

x1
x2
x3
x4
x5
x6

solve(t(x1)%*%x1)
solve(t(x2)%*%x2)
solve(t(x3[,-3])%*%x3[,-3])
solve(t(x4[,-3])%*%x4[,-3])
solve(t(x5[,-3])%*%x5[,-3])
solve(t(x6[,-3])%*%x6[,-3])

g1=c(1,0,0,0)
t(g1)%*%solve(t(x1)%*%x1)%*%g1
t(g1)%*%solve(t(x2)%*%x2)%*%g1

g2=c(0,0,1,0)
t(g2)%*%solve(t(x1)%*%x1)%*%g2
t(g2)%*%solve(t(x2)%*%x2)%*%g2

g3=c(0,1,0,1)
t(g3)%*%solve(t(x1)%*%x1)%*%g3
t(g3)%*%solve(t(x2)%*%x2)%*%g3

g4=c(0,0,1,.5)
t(g4)%*%solve(t(x1)%*%x1)%*%g4
t(g4)%*%solve(t(x2)%*%x2)%*%g4

g5=c(0,1,0,.5)
t(g5)%*%solve(t(x1)%*%x1)%*%g5
t(g5)%*%solve(t(x2)%*%x2)%*%g5