Matrices 2014.notebook

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March 27, 2014

1.  ­2 5.  ­36

2.  ­6 6.  0

3.  25 7.  ­131

4.  0 8.  120

Homework Solutions #1­ 8 

Cramer's Rule

Matrices 2014.notebook

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March 27, 2014

In linear algebra, Cramer's rule is a theorem, which gives an expression for the solution of a system of linear equations with as many equations as unknown variables. The solution is expressed in terms of the determinants of the coefficient matrix. This rule is named after Gabriel Cramer.

Steps to Cramer's Rule:1. Create a rectangular 2 x 3 matrix. Label your columns.2. Create a square matrix with "x" and "y" columns and solve for D.3. Create a square matrix with "#" and "y" columns and solve for Dx. The variable you are solving for is replaced in the matrix with the #.4. Create a square matrix with "x" and "#" columns and solve for Dy. The variable you are solving for is replaced in the matrix with the #. 5. Solve for x = and y =6. Check!

I can solve a 2 by 2 system using determinants.

#  y x  #x  y

x    y      #

I can set up the determinants to solve a 2 by 2

Matrices 2014.notebook

3

March 27, 2014

Example #1: Solve the system of equations using Cramer's rule. x + 2y = 5x - 2y = 9

I can solve a 2 by 2 system using determinants.

Solution on next slide...

Example #1: Solve the system of equations using Cramer's rule. x + 2y = 5x - 2y = 9

# y x #x y

I can solve a 2 by 2 system using determinants.

x y #

Matrices 2014.notebook

4

March 27, 2014

Example #2: Solve the system of equations using Cramer's rule. x - 4y = 293x + 2y = -11

I can solve a 2 by 2 system using determinants.

Solution on next slide...

Example #2: Solve the system of equations using Cramer's rule. x - 4y = 293x + 2y = -11

#  y x  #x  y

# y x #x y

I can solve a 2 by 2 system using determinants.

x  y  #

Matrices 2014.notebook

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March 27, 2014

x  #x  y #  y

Example #3: Solve the system of equations using Cramer's rule. 4x + 3y = -43x - 7y = 34

# y x #x y

I can solve a 2 by 2 system using determinants.

x  y  #

Homework:#1 - 5

Matrices 2014.notebook

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March 27, 2014

HomeworkSolve using Cramer's Rule (matrices) and check.1.

2.

3.

HomeworkSolve using Cramer's Rule (matrices) and check.4.

5.