Matrices
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'Matrix calculator' data sets are designed to handle matrix computations.

Up to five Matrices are defined in the Matrix Editor tab. (Described below).  Once defined, you type matrix expressions to be evaluated in the Program tab, using variables to represent the matrices. A full range of matrix operations are supported, and results appear on the text view.

Program tab

Type matrix expressions and other commands in the 'Program tab'. You can even program loops for generating matrix series.

This example is a program included with Maths Helper Plus. It solves simultaneous linear equations in any number of unknowns. You use the 'Matrix Editor' tab to input the equation coefficients in matrix 'A', and the right side values as a column matrix 'B'. Click the 'Run' button to view the solutions on the text view.

For example, consider these linear equations:

  2x + 3y z = 7
      4y + 6z = 26
5x + 9y + 2z = 7

Then the coefficient matrix, 'A' is:

2   3  -1
0  -4   6
5   9   2

and the column matrix 'B' of right side values is:

-7

The solutions appear on the text view like this:

Output
Solve the linear equations
with coefficients:
A = 2  3 -1
    0 -4  6
    5  9  2
and right side values:
B = -7
    26
    -7
 Then the solutions:
    x
    y
    z
 are as follows:
X = 1
   -2
    3

Matrix Editor

This options tab has a large edit box where you enter and edit matrices.

Type the elements of your matrix with commas between them, like this:

1, 2, 3
4, 5, 6
7, 8, 9

Use expressions for the elements, like this:

2/3, 3/4, 5/8
pi/4, pi/3, pi/7
sin25, cos25, tan25

To enter large matrices quickly, take advantage of the following short cuts:

  1. A blank line is filled with zero elements.

  2. A comma with nothing to the left of it is the same as zero.

  3. Unfinished lines are finished off with zero elements if there is another line with more elements. The longest line entered determines how many zeros are required.

For example, enter this:

1,2
<blank line>
,,,,,3,,4

to get this:

1, 2, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 3, 0, 4

 

2 by 2 Matrix Calculations

This tab has options to create working steps for basic matrix operations on matrices 'A' and 'B'. The options are only available for 2 by 2 matrices.

Here is a sample output created by this option:

Calculations for 22 matrices
Matrix A = [ a11 a12 ]
           [ a21 a22 ]

         = [ 1 2 ]
           [ 3 4 ]

The DETERMINANT of A is given by:

     Det = a11a22 - a12a21
         = 1 4 - 2 3
         = -2

The INVERSE of A is given by:

    invA = [ a22/Det -a12/Det ]
           [ -a21/Det a11/Det ]
         
         = [ -2     1 ]
           [ 1.5 -0.5 ]

Matrix B = [ b11 b12 ]
           [ b21 b22 ]

         = [ 5 6 ]
           [ 7 8 ]

Matrix Addition:

   A + B = [ (a11+b11) (a12+b12) ] = [ p q ]
           [ (a21+b21) (a22+b22) ]   [ r s ]

 then: p = 1 + 5
         = 6
       q = 2 + 6
         = 8
       r = 3 + 7
         = 10
       s = 4 + 8
         = 12
so A + B = [ 6   8 ]
           [ 10 12 ]


Matrix Multiplication:

   A B = [ (a11b11)+(a12b21) (a11b12)+(a12b22) ]
           [ (a21b11)+(a22b21) (a21b12)+(a22b22) ]

         = [ p q ]
           [ r s ]

 then: p = (15)+(27)
         = 19
       q = (16)+(28)
         = 22
       r = (35)+(47)
         = 43
       s = (36)+(48)
         = 50
so A B = [ 19 22 ]
           [ 43 50 ]