Transcript Lesson 4-6: Using Matrices to Solve Equations

A basic equation is made of three parts,
coefficients, variables, and the
constants.
 The coefficient is the number before the
variable
 The variable is the letter of which you are
trying to find the value
 And the constant is what the equation is
equal to.

7x+5y=3
 3x-2y=22
 To find the answer to these equations
you can use matrices.
 The coefficients go in one matrix, you
multiply that by the variable matrix, and
then set the two equal to the constants.

7x+5y=3
 3x-2y=22

 7 5   x  3 
x

3 2  y   22
    


To solve without a calculator you must
first find the inverse:
 2
1 /  14  (15)  
 3
or
 2
1 /  29  
 3
5 

7 
5 

7 
 2 5 7 5   x 
 2 5 3 
 1 / 29  

    1 / 29  
 



 3 7  3  2  y 
 3 7  22
 29 0   x 
 2 5 3 
 1 / 29  
    1 / 29  
 


0  29  y 
 3 7  22
1 0  x 
4 
0 1   y     5

  


x 
4 
 y     5
 


Is then (4,-5)
 Aren’t you glad you have a TI
calculator?
 You don’t ever have to do that long
process ever again!

Click:
 2nd
 Matrix
 Edit
A


Put in dimensions for the equation (2x2 3x3,
etc) under A (use 2x2 for this example)

Type in the coefficient matrix as it
appears.








Repeat the first three steps except put the
constant matrix under B.
Exit out of the matrix (2nd, quit)
Then click 2nd, and then Matrix
Select A
Then hit the “x-1” button to get the inverse
Then multiply that by the matrix B
And Voila! You have your X and Y!
Make sure when you are typing in the numbers
for your matrices that the dimensions are
correct, the number of columns goes first, then
the number of rows.
Solve:
 8x+3y-65z=46
 6y+18z=34
 21x+40y=89z+12
 HAVE FUN!


No problem!

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