HP 49g Characterizing a matrix The matrix Norm menu, Solution of linear systems, Function DET

Characterizing a matrix (The matrix NORM menu)

The matrix NORM (NORMALIZE) menu is accessed through the keystroke

sequence . This menu is described in detail in Chapter 10 of the calculator’s„´User’s Guide. Some of these functions are described next.

Function DET

Function DET calculates the determinant of a square matrix. For example,

Function TRACE

Function TRACE calculates the trace of square matrix, defined as the sum of the elements in its main diagonal, or

tr(A) = ∑n aii .

i=1

Examples:

Solution of linear systems

A system of n linear equations in m variables can be written as

a11⋅x1	+ a12⋅x2	+ a13⋅x3	+ …+ a1,m-1⋅x m-1		+ a1,m⋅x m	= b1,
a21⋅x1	+ a22⋅x2	+ a23⋅x3	+ …+ a2,m-1⋅x m-1		+ a2,m⋅x m	= b2,
a31⋅x1	+ a32⋅x2	+ a33⋅x3	+ …+ a3,m-1⋅x m-1		+ a3,m⋅x m	= b3,
.	.	.	…	.	.	.

an-1,1⋅x1 + an-1,2⋅x2 + an-1,3⋅x3 + …+ an-1,m-1⋅xm-1 + an-1,m⋅xm = bn-1,an1⋅x1 + an2⋅x2 + an3⋅x3 + …+ an,m-1⋅xm-1+ an,m⋅x m = bn.

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