D1

Solve the given matrix equation for x or explain why no solution exists. x*A -B = C

A <- matrix(c(3,1,2,0,1,4),nrow = 3,ncol = 2)
B <- matrix(c(4,1,3,2,0,1),nrow = 3,ncol = 2)
C <- matrix(c(2,1,1,-2,2,6),nrow = 3,ncol = 2)
A

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

B

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

C

##      [,1] [,2]
## [1,]    2   -2
## [2,]    1    2
## [3,]    1    6

multiplying x with matrix A would give us equations

(3*x) - 4 = 2

x - 1 = 1 Equation 1

(2*x) - 3 = 1

    -2 = -2
    
     x = 2
     
4x - 1 = 6  Equation 2 

solving two equations we get two values for x(x = 2,x = 7/4),and therefore we say that system has no solution.