1 Simultaneous Equations

Consider the following system of linear equations:

Recall from MATH105 that this system can be represented by the augmented matrix:

The square matrix on the left-hand-side is equal to matrix $A$ from the introduction to this workshop and the right-hand-side vector is created in RStudio by:

b <- c(0, -8, 4)

One method that calculates the solution to this system of linear equations is to pre-multiply this vector by the inverse of matrix $A$. We can find the inverse by using the function solve introduced in last week’s workshop.

Ainv <- solve(A)

Ainv %*% b

Alternatively, we can use the solve command by supplying two arguments; the first being the square matrix and the second being the vector:

solve( A, b )