# 3x3 Matrices

Document Sample

```					  3x3 matrices
IB SL/HL maths

www.ibmaths.com
3x3 Matrices
By the end of this lesson you will be able to:
•   find the determinant of a 3x3 matrix
without a GDC.
•   find inverses and determinant of 3x3
matrices using a GDC.
•   solve simultaneous equations using in
3 or more unknowns using a GDC.
Determinant of a 3x3 matrix without a GDC
 b c
a
     
d
det e f  a(ei  fh)  b(di  fg)  c(dh  eg)
 h i 
g
     

Sometimes this is better seen and remembered by using a
diagram:


-               +

Highlight a, then cancel the numbers in a’s column and row.
Find the determinant of the 2x2 matrix remaining.
Continue for b and c. Remember to subtract b.
Now some practise…
Find the determinants of each matrix.
1 2 3 
      
A  
2 0 2                  A  60
7 3 5
      
8 1 9 
       
B  3 0 1                  B  104
2 3 1 

         
1 3 4 

       
C  
2 2 1                   C  41
        
1 2 3 
       
2 1 1
Using your GDC to get the                                 
determinant.                                         2 0 1 
A  
1 3 2
The TI
      
The Casio
1.Enter a 3x3 matrix.
1. From the main menu choose
Go to the Matrix function by          Matrix option, choose a
2nd x-1.                            matrix and set it’s
Tab across to Edit, and ENTER.        dimensions.

Choose the dimensions: 3x3, and       Enter the matrix.
2. Quit when you have entered          and go into Run.
your matrix. Go back into the     3. Choose OPTN, F2, F3
Matrix function, and tab across      (Det), then F1 (Mat),
to MATH, choose option 1; now        ALPHA, and choose the
go back to Matrix and choose A.      matrix you entered.
2 1 1
Using your GDC to get the inverse                        
of a 3x3 matrix.                                    2 0 1 
A  
1 3 2
      
The TI
The Casio
1. Enter the matrix as before.
1. Enter the matrix as before.
2. Go into the Matrix menu and     
select matrix from the first    2. Go into the Run menu, and
menu.                              choose OPTN, followed by F2
and F1, ALPHA and choose
3. Now select the x-1 and ENTER.
the matrix.
4. To get the numbers as
3. When the matrix is on the
fractions you must now enter
screen put it to the power of
ANS FRAC (from the MATH
negative 1.

Ensure that you use SHIFT ) and
not ^ button.
2 1 1
Solving a simultaneous equation with                                  
2 0 1 
A  
3 unknowns.                                                     1 3 2
      
Solve these simultaneous equations:                      5 
x
   
y      6
A   
2x  y  z  5
             
z      3
2x  z  6                                            
x  3y  2z  3                             Remove the A by multiplying
Look at the simultaneous equations             both sides by A-1.
and it could be written as:                             1  1 
  1       

x          3  3  5 

2 1 1x  5                                      
y      1
     1 0 6

       
                                
z          5  2  

6
2 0 1 y                              2      3

                                                      3  3 


1 3 2 z   
3
       
                        Now on your GDC multiply

the two matrices to give the
This can be written as:                   values: x=4, y=-1, z=2
Now solve these equations:

1.   xy z  6
x  2y  3z  11       x  2,y  3, z  1
4x  3y  2z  1

2x  y  z  4
2.                             1    1      5
x  2y  z  4         x  ,y  , z 

3x  y  2z  6
        2    2      2
x  y  z  2
3.
3x  4y  z  1

               ,
x  3,y  1 z  6
2x  5y  2z    13

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 25 posted: 10/3/2012 language: English pages: 8
How are you planning on using Docstoc?