Problem c10 on Page 44

The augmented matrix for problem C10 looks as follows: 2 -3 1 7 | 14
2 8 -4 5 | -1
1 3 -3 0 | 4
-5 2 3 4 | -19

The final matrix will appear here, followed by the code to reduce the matrix:

##      [,1] [,2] [,3] [,4] [,5]
## [1,]    1    0    0    0    1
## [2,]    0    1    0    0   -3
## [3,]    0    0    1    0   -4
## [4,]    0    0    0    1    1

X1= 1
X2= -3
X3= -4
X4= 1

ourMatrix<-matrix(c(2,2,1,-5,-3,8,3,2,1,-4,-3,3,7,5,0,4,14,-1,4,-19),nrow=4)


for(j in 2:4)               {
for(i in 5:1)      {
ourMatrix[j,i]<-((ourMatrix[j,i]*ourMatrix[1,1]/ourMatrix[j,1]*-1)+ourMatrix[1,i])
                   }
                            }

for(j in c(1,3,4))               {
for(i in c(1,3,4,5,2))      {
ourMatrix[j,i]<-((ourMatrix[j,i]*ourMatrix[2,2]/ourMatrix[j,2]*-1)+ourMatrix[2,i])
                   }
                            }

for(j in c(1,2,4))               {
for(i in c(1,2,4,5,3))      {
ourMatrix[j,i]<-((ourMatrix[j,i]*ourMatrix[3,3]/ourMatrix[j,3]*-1)+ourMatrix[3,i])
                   }
                            }
for(j in c(1,2,3))               {
for(i in c(1,2,3,5,4))      {
ourMatrix[j,i]<-((ourMatrix[j,i]*ourMatrix[4,4]/ourMatrix[j,4]*-1)+ourMatrix[4,i])
                   }
                            }

for(i in 1:4)    {
ourMatrix[i,5]<-ourMatrix[i,5]/ourMatrix[i,i]

for(j in 1:4)           {
ourMatrix[i,j]<-0
ourMatrix[i,i]<-1
                       }
}
ourMatrix