Mathc : The news group of this work.
Presentation of the functions:
matrxf.zip
: You can work with fractions.
addm, subm, multm, powm, smultm, transpose, trace,
det, minor, mminor, cofactor, mcofactor, adjoint,
inverse, inverse(gaussjordan), gauss, gaussjordan.
matrxg.zip
: You can also work with integers.
matrxh.zip
: Useful Functions.
In this section, the size of the matrices,
are randomly selected by the computer,
but you can selecte the size if you want.
Verify with numeric applications:
mtrxaa.zip
: How to use the basic functions.
mtrxab.zip
: the properties of matrix arithmetic.
A+B = B+A
(A+B)+C = A+(B+C)
(AB)C = A(BC)
A(B+C) = AB+AC
(B+C)A = BA+CA
A(B-C) = AB-AC
(B-C)A = BA-CA
a(B+C) = aB+aC
a(B-C) = aB-aC
(a+b)C = aC+bC
(a-b)C = aC-bC
a(bC) = (ab)C
mtrxac.zip
:
* The properties of zero matrices.
* The properties of the transpose.
* The theorem of transpose.
* The theorem of inverse matrices.
mtrxad.zip
:
* (A+B)**2.
* (A-B)**2.
* (A-B) (A+B).
* Power and inverse.
* Symetric and Skew-Symetric matrices.
mtrxae.zip
:
* Solving linear systems by matrix inversions.
* Linear systems with common coefficient matrix.
mtrxaf.zip
:
* The system of equation Ax = b is consistent.
* Inverses of symmetric matrices.
* Power, inverse of diagonal matrices
* Multiply, inverse of triangular matrices.
* Trace property.
mtrxag.zip
: the value of the determinant of
* a diagonal matrix
* a triangular matrix (upper, lower)
* a basic matrix.
Application:
mtrxid.zip
: Identity matrix application I
* Swap two rows.
* The pivot value.
* Eliminate the coefficient below, above, the pivot.
* Gauss Jordan elimination with the help of the identity matrix.
* Inverse of the matrix with the help of the identity matrix.
mtrxic.zip
: Identity matrix application II<
* The work on a column in one step.
* All the values below the pivot in one step.
* Application : Gauss elimination.
* All the values above the pivot in one step.
* Application : Gauss Jordan elimination
* Application : Inverse of the matrix
mtrxgo.zip
: Geometric application.
* Find the coefficients of a polynome,
that passes through three, four, five points.
* Find the coefficients a, b, c, d, e of a conic,
ax**2 + by**2 + cx + dy + e = 0
that passes through four points.
* Find the coefficients a, b, c, d of a circle,
a(x**2 + y**2) + bx + cy + d = 0
that passes through three points.
mtrxch.zip
: Chemistry application.
* Find the coefficients of a chemical equation.
mtrxsy.zip
: Resolve some nonlinear systems of equations.