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Page 11-41
The result (A
-1
)
n×n
= C
n×n
/det(A
n×n
), is a general result that applies to any
non-singular matrix A. A general form for the elements of C can be written
based on the Gauss-Jordan algorithm.
Based on the equation A
-1
= C/det(A), sketched above, the inverse matrix,
A
-1
, is not defined if det(A) = 0. Thus, the condition det(A) = 0 defines also a
singular matrix.
Solution to linear systems using calculator functions
The simplest way to solve a system of linear equations, A⋅x = b, in the
calculator is to enter b, enter A, and then use the division function /. If the
system of linear equations is over-determined or under-determined, a “solution”
can be produced by using Function LSQ (Least-SQuares), as shown earlier. The
calculator, however, offers other possibilities for solving linear systems of
equations by using Functions included in the MATRICES’ LINEAR SYSTEMS..
menu accessible through „Ø(Set system flag 117 to CHOOSE boxes):
The functions included are LINSOLVE, REF, rref, RREF, and SYST2MAT.
Function LINSOLVE
Function LINSOLVE takes as arguments an array of equations and a vector
containing the names of the unknowns, and produces the solution to the linear
system. The following screens show the help-facility entry (see Chapter 1) for
function LINSOLVE, and the corresponding example listed in the entry. The
right-hand side screen shows the result using the line editor (press ˜ to
activate):
Here is another example in ALG mode. Enter the following: