Exercise C19

A <- matrix(c(2,1,-1,-1,3,4,3,5),4,2,byrow = TRUE)
b <- c(6,-2,4,2)
showEqn(A, b)

##  2*x1 + 1*x2  =   6 
## -1*x1 - 1*x2  =  -2 
##  3*x1 + 4*x2  =   4 
##  3*x1 + 5*x2  =   2

c( R(A), R(cbind(A,b)) )          # show ranks

## [1] 2 2

all.equal( R(A), R(cbind(A,b)) )  # consistent?

## [1] TRUE

# Plot the equations:

plotEqn(A,b)

## 2*x1   + x2  =   6 
##  -x1 - 1*x2  =  -2 
## 3*x1 + 4*x2  =   4 
## 3*x1 + 5*x2  =   2

Solve(A, b, fractions = TRUE)

## x1    =   4 
##   x2  =  -2 
##    0  =   0 
##    0  =   0

The solution is 4,-2,0,0

DATA 605 Week 1 EXERCISE SOLUTION