MATH1012 - Lecture 2

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MATH1012 - Lecture 1

Vital Point

• All non-basic variables are free variables
• All basic variables are linear combinations of constants and free variables
  • e.g. $x_1$ is a basic variable defined as $x_1=1-x_2$
  • Leading entries will become basic variables

Always want to achieve row-echelon form and then we can systematically solve the matrix

Summary of Gaussian Elimination Method

• Write system of equations in augmented matrix
• Use Gaussian elimination to convert into row echelon form
• Identify leading entries and basic and non-basic variables

Matrix Notation

When showing working during Gaussian Elimination, show that you have changed the row by writing the way you reduced it ‘overwriting’ the original row.

e.g. R${}_n$ ← R${}_n$ - kR${}_{n-1}$

For the next overwrite, R$n$ will represent what it equalled in the recent matrix and this will simplify your working.

e.g. write R${}_{n+1}$ ← $x$R${}_n$ instead of R${}_{n+1}$ ← $x$(R${}_n$ - 3R${}_{n-1}$)

Read slides for more information on reduced row-echelon form

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Annotated Slides