MATRIX Course

Example

Go back

In the previous example, we had rewritten the given system, and it gave us the matrix $A$, and the vector $b$.

\[ A = \begin{split}\begin{pmatrix} 1 & -1 & 2\\ 1 & 2 & 0 \end{pmatrix} \quad b = \begin{pmatrix}3 \\ 0\end{pmatrix} \end{split} \]

Solving using GAUSS

We used the GAUSS method (you got more methods in the numerical analysis course), which could be coded as follows in R

library('matlib')

A <- matrix(c(1,-1,2,1,2,0), nrow = 2, byrow = T)
b <- c(3,0)

gaussianElimination(A, b)
#      [,1] [,2]       [,3] [,4]
# [1,]    1    0  1.3333333    2
# [2,]    0    1 -0.6666667   -1
# [3,]    0    0  0.0000000    0

Results

We are converting our matrix back to a system

  • $x_1 = 2 - \frac{4}{3} x_3$
  • $x_2 = -1 + \frac{2}{3} x_3$