# Solve a system of linear equations

# Define A matrix and b vector from Section 2.10 in the notes

A <- matrix(c(2, 3, 3, -6), 2, 2)

b <- matrix(c(5, -3), 2, 1)

# check the determinant

det(A)

# obtain the inverse

Ainv=solve(A)

# get the solution

Ainv %*% b

# or do it in one step

solve(A) %*% b

# or do it "the long way"

A2 <- matrix(c(-6, -3, -3, 2), 2, 2)

1/(det(A))*A2 %*% b