Download Inverse of a Matrix and Sys of Eq

Section 10.3 and Section 9.3
Systems of Equations and Inverses of Matrices
NO CALCULATOR
2x  7y  4
Given the system of equations 
3x  4y  6
A) Set up a matrix equation to solve the system.
2 7   x   4 
3 4   y    6 

   
B) Solve the matrix equation, writing your final answer as an
ordered pair (x, y). Show the work that leads to your answer.
1
 x  2 7   4 
 y   3 4   6 
  
  
 x  1 58
 y   29  0 
 
 
 x  1  4 7  4
 y   29  3 2  6 
 

 
 2, 0 
NO CALCULATOR
3x  2y  1
Given the system of equations 
4x  3y  5
A) Set up a matrix equation to solve the system.
3 2  x   1
 4 3   y   5 

   
B) Solve the matrix equation, writing your final answer as an
ordered pair (x, y). Show the work that leads to your answer.
1
 x  3 2  1
 y    4 3  5 
  
  
 x  1 13 
 y   17 11
 
 
 x  1  3 2  1
 y   17  4 3  5 
 

 
 13 11 
 17 , 17 


NO CALCULATOR
5x  4y  1
Given the system of equations 
3x  2y  2
A) Set up a matrix equation to solve the system.
 5 4  x   1 
 3 2   y    2

   
B) Solve the matrix equation, writing your final answer as an
ordered pair (x, y). Show the work that leads to your answer.
1
 x   5 4  1 
 y    3 2   2
  
  
 x  1 2 4   1 
 y   22 3 5   2
 

 
 x  1 10 
 y   22  7 
 
 
 5 7 
 11, 22 


NO CALCULATOR
5x  4y  1
Given the system of equations 
3x  2y  2
A) Set up a matrix equation to solve the system.
 5 4  x   1 
 3 2   y    2

   
B) Solve the matrix equation, writing your final answer as an
ordered pair (x, y). Show the work that leads to your answer.
1
 x   5 4  1 
 y    3 2   2
  
  
 x  1 2 4   1 
 y   22 3 5   2
 

 
 x  1 10 
 y   22  7 
 
 
 5 7 
 11, 22 


CALCULATOR REQUIRED
Enter the following matrices into your calculator:
3 1
A

2
7


 3 7 1
E   7 0 3 


 8 1 4 
9 
7
C

11

16


 1 4 2
F   3 5 1 


 0 0 2 
 2 1
D

4

2


11 2 3 
G   4 3 2 


 1 2 4 
CALCULATOR REQUIRED
3x  y  7
Using a calculator, solve the system: 
2x  7y  4
3 1
is already entered into your calculator
A

2 7 
7 
B    needs to be entered into your calculator [B]
4
Compute det A
Compute 19  A 1B
 45 2 
 19 , 19 


CALCULATOR REQUIRED
7x  9y  2
Using a calculator, solve the system: 
11x  16y  5
9 
7
is already entered into your calculator
C

11 16 
 2
B    needs to be entered into your calculator [B]
5 
Compute det C
Compute 211 C1B
 77 13 
 211, 211 


CALCULATOR REQUIRED
2x  y  14
Using a calculator, solve the system: 
4x  2y  28
 2 1
is already entered into your calculator
D

 4 2
14 
B    needs to be entered into your calculator [B]
28 
Compute det D
Since det D = 0,
There is
NO UNIQUE SOLUTION
CALCULATOR REQUIRED
3x  7y  z  1

Using a calculator, solve the system: 7x  3z  4
8x  y  4z  2
3
7
1



E   7 0 3  is already entered into your calculator


 8 1 4 
1
B   4  needs to be entered into your calculator [B]
 
 2
Compute 348  E1B
 153 100 107 
 348 , 348 , 348 


CALCULATOR REQUIRED
 x  4y  2z  5

Using a calculator, solve the system:3x  5y  z  2
2z  7
1
4

2



F   3 5 1 is already entered into your calculator


 0 0 2 
5
B   2 needs to be entered into your calculator [B]
 
 7 
Compute 34  F1B
 164 61 119 
 34 , 34 , 34 


CALCULATOR REQUIRED
11x  2y  3z  0

Using a calculator, solve the system: 4x  3y  2z  1
 x  2y  4z  2
1
4

2



G   3 5 1 is already entered into your calculator


 0 0 2 
0 
B   1 needs to be entered into your calculator [B]
 
 2 
Compute 75  G1B
 12 21 30 
 75 , 75 , 75 

