Solving linear systems using Cramer's Rule - Matrices

Solving linear systems using Cramer's Rule

Last chapter we saw that we are able to solve linear systems with Gaussian Elimination. Now we are going to take a look at a new method which involves solving linear systems with Cramer's Rule. Cramer's Rule requires us to find the determinant of 2 x 2 and 3 x 3 matrices (depends on your linear system). However, this rule can only be used if you have the same number of equations and variables. If you have a different number of equations and variables, then finding the determinant will be impossible. Hence, it will not be possible to use Cramer's rule.

Lessons

Notes:

This is a different way of solving linear systems. Instead of using Gaussian Eliminations, you can use Cramer’s Rule! Make sure to review your determinants of 2 x 2 and 3 x 3 matrices.

Cramer’s Rule for 2 x 2 matrices:

$x=\frac{D_x}{D}$

$y=\frac{D_y}{D}$

Cramer’s Rule for 3 x 3 matrices:

$x=\frac{D_x}{D}$

$y=\frac{D_y}{D}$

$z=\frac{D_z}{D}$

Intro Lesson

Cramer’s Rule Overview:
1.
Cramer’s Rule with 2 x 2 matrices
Solve the following linear systems with Cramer’s Rule”
2.
Cramer’s Rule with 3 x 3 matrices
Solve the following linear systems with Cramer’s Rule”