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Working with Matrices
 

Matrices are rectangular arrays of elements. 
The dimension of a matrix is the number of rows by the number of columns.

Adding Matrices - matrices must be of the same dimension to be added.
                               Add:  m1


First Enter the Matrices (one at a time):

Step 1:  Go to Matrix
                 (above the  x-1 key) 
d2
If dimensions appear next to the names of the matrices, such as 3x3, a matrix is already stored in the calculator.  You may save it by moving to a new name, or overwrite it.
 

Step 2:  Arrow to the right to
             EDIT to allow for
             entering the matrix.

  d3

Step 3:  Type in the dimensions (size) of your matrix and enter the elements (press ENTER).    
  m2

Step 4:  Repeat this process for
              the second matrix

. m3

Step 5: Arrow to the right to
             EDIT and choose a
             new name.

  m4

Step 6:  Type in the dimensions (size) of your matrix and enter the elements (press ENTER).     m5

Now, add:
Step 7: 
Return to the home
              screen.  Go to Matrix
            
 to get the names of the
              matrices for adding.

  m6

 

The answer to the addition, as seen on the calculator screen,
 is =

m7

 

 

Multiplying Matrices- for multiplication to occur, the dimensions of the matrices must be related in the following manner:  m x n  times  n x r  yields  m x r
                               Multiply: m8
First Enter the Matrices (one at a time) as shown above:

Step 1:   Once the matrices are entered, you should see their dimensions in residence when you go to Matrix  (above the  x-1 key) 
 m9
 
Step 2:   Return to the home
              screen.  Go to Matrix
            
 to get the names of the
              matrices for multiplying.

  m10


The product, as seen on the calculator screen,
 is =

m11

 

Using Matrices to Solve Systems of Equations:

1.  (using the inverse coefficient matrix)
Write this system as a matrix equation and solve:  3x  + 5y = 7 and 6x - y = -8

Step 1:  Line up the x, y and
              constant values.

         3x  + 5y =  7
         6x   -   y = -8

 

Step 2:  Write as equivalent
              matrices.

       m17

Step 3:  Rewrite to separate out
              the variables. 

m18

Step 4:  Enter the two numerical matrices in the calculator.
 m14
Step 5:  The solution is obtained by multiplying both sides of the equation by the inverse of the matrix which is multiplied times
the variables.

   m19
Step 6:  Go to the home screen and enter the right side of the previous equation.
  m16


 


The answer to the system, as seen on the calculator screen,
 is  x = -1 and y = 2.

Note: If the determinant of a matrix is zero, the matrix does not have an inverse. Thus, a single point, (x,y), solution cannot be found.


2.  (using Gauss-Jordan elimination method with reduced row echelon form )
    
Solve this system of equations:
2x - 3y + z = -5
4x y - 2z = -7
-x + 2z = -1

 
Step 1:  Line up the variables and
              constants
     2x - 3y  + z = -5
     4x y  - 2z = -7
     -x + 0y + 2z = -1

Step 2:  Write as an augmented
              matrix and enter into
              calculator.
       m20

Step 3:  From the home screen, choose the rref function.  [Go to
Matrix  (above the  x-1key), move right→MATH, choose B: rref]

  m21
Step 4:  Choose name of matrix
             and hit ENTER.
 m22
Step 5:  The answer to the system, will be the last column on the calculator screen:
          x = -3
          y = -1
          z
= -2.
 


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