discussion posts

Solving the problem posted by Jacob Silver: C31

Question C31 asks to solve the following set of linear equations:

3x + 2y = 1 x - y = 2 4x + 2y = 2

To solve this, we can use the matrix form of the equations:

Matrix A:

\[ A = \begin{pmatrix} 3 & 2 \\ 1 & -1 \\ 4 & 2 \end{pmatrix} \]

Matrix B:

\[ B = \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix} \]

To solve this in R, since this is an over-determined system (more equations than unknowns), I’ll use the MASS package:

library(MASS)

# matrix of coefficients A and the constant vector B
A <- matrix(c(3, 2, 1, -1, 4, 2), nrow = 3, byrow = TRUE)
B <- c(1, 2, 2)

# pseudoinverse of A
A_pinv <- ginv(A)

# solving for x
x <- A_pinv %*% B

print(x)

##      [,1]
## [1,]    1
## [2,]   -1