Introduction to Systems of Linear Equations

System of Linear Equations & Gaussian Elimination (G.E.)

To solve a system of linear equations using G.E., it is important that you really understand few concepts like knowing how to identify linear equations, recognize a matrix in row echelon form, and differentiate among the types of solutions for linear systems using rank concept.

Let's try this quiz together!

Multiple Select

Which of the following is a linear equation in 

$$x_1,\ x_2,\ x_3$$ ?

• $$x_1-5x_2+8x_1x_3=10$$  

• $$\sqrt{5}x_1+\pi x_2-\frac{1}{4}x_3=6^{\frac{1}{3}}$$  

• $$x_1=-x_2+3x_3^2$$  

• $$-x_1-\frac{1}{x_2}+x_3=0$$  

That's a piece of cake?!

More to come...

Multiple Choice

Is this a matrix in row echelon form (r.e.f.)?

• Yes

• No

Multiple Choice

Is this augmented matrix in its row echelon form (r.e.f.)?

• Yes

• No

More to come...

My lecturer: Okay, another wave is coming your way~

Me: Bring it on!

Fill in the Blank

This augmented matrix is in row echelon form (r.e.f.). Its r([A|b]) is ___.

Multiple Choice

We use Gaussian Elimination to ...

• change the solutions or the non-solvability of a system of linear equations.

• change the rank of a system of linear equations.

• check the linear dependence/ independence of a system of linear equations.

• reduce an augmented matrix to row echelon form.

Here's the final wave!

Me: I'm ready for that!!!

Multiple Choice

Systems of linear equations can have all the following solutions, except _____.

• a unique solution.

• exactly two different solutions.

• infinitely many solutions.

• no solutions at all.

Multiple Select

Given an augmented matrix in r.e.f., which are the non-leading variable?

• $$x_1$$

• $$x_2$$

• $$x_3$$

• $$x_4$$

Good job! You killed it!

You should be able to understand all the contents of Lecture 7 by now. Do practice more to up-level yourself from beginner to intermediate. Have fun with Gaussian Elimination. Ciao!

Cheers,

Loh