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Solving linear systems using Cramer's Rule
- Intro Lesson: a12:16
- Intro Lesson: b20:57
- Lesson: 1a8:41
- Lesson: 1b7:47
- Lesson: 1c8:31
- Lesson: 1d6:59
- Lesson: 2a17:55
- Lesson: 2b19:48
- Lesson: 2c22:07
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.
Basic Concepts: Solving a linear system with matrices using Gaussian elimination, The determinant of a 2 x 2 matrix, The determinant of a 3 x 3 matrix (General & Shortcut Method)
Lessons
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=DDx
y=DDy
Cramer's Rule for 3 x 3 matrices:
x=DDx
y=DDy
z=DDz
Cramer's Rule for 2 x 2 matrices:
x=DDx
y=DDy
Cramer's Rule for 3 x 3 matrices:
x=DDx
y=DDy
z=DDz
- IntroductionCramer's Rule Overview:a)Using Cramer's Rule with 2 x 2 matricesb)Using Cramer's Rule with 3 x 3 matrices
- 1.Cramer's Rule with 2 x 2 matrices
Solve the following linear systems with Cramer's Rule"a)x+2y=3
2x+3y=1b)5x+3y=1
x+y=2c)y=3x+5
y=4x−2d)2x+4y=3
4x+8y=6 - 2.Cramer's Rule with 3 x 3 matrices
Solve the following linear systems with Cramer's Rule"a)x+4y+3z=1
x+2y+9z=1
x+6y+6z=1b)x+3y+4z=4
−x+3y+2z=2
3x+9y+6z=−6c)2−3y−3z=x
3x+9y=3−3z
3x+6y+6z−4=0
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23.
Determinants and Inverses of Matrices
23.1
The determinant of a 2 x 2 matrix
23.2
The determinant of a 3 x 3 matrix (General & Shortcut Method)
23.3
The inverse of a 2 x 2 matrix
23.4
The inverse of 3 x 3 matrices with matrix row operations
23.5
The inverse of 3 x 3 matrix with determinants and adjugate
23.6
2 x 2 invertible matrix
23.7
Solving linear systems using Cramer's Rule
23.8
Solving linear systems using 2 x 2 inverse matrices