Reference Guide

ManualsBrandsHP ManualsCalculators, organizers50g Graphing Calculator

171

172

173

174

175

176

177

178

179

180

Full Command and Function Reference 3-57

(See the description of dn and Chapter 16 of the User’s Guide for an explanation of the use of

“d1” for a derivative.)

Result:

{Y(X)=(1/5*EXP(5*X)+cC0)*(1/EXP(X)^2)}

See also: dn, LDEC

DET

Type: Command

Description: Determinant Function: Returns the determinant of a square matrix.

The argument matrix must be square. DET computes the determinant of 1 × 1 and 2 × 2

matrices directly from the defining expression for the determinant. DET computes the

determinant of a larger matrix by computing the Crout LU decomposition of the matrix and

accumulating the product of the decomposition’s diagonal elements.

Since floating-point division is used to do this, the computed determinant of an integer matrix is

often not an integer, even though the actual determinant of an integer matrix must be an integer.

DET corrects this by rounding the computed determinant to an integer value. This technique is

also used for noninteger matrices with determinants having fewer than 15 nonzero digits: the

computed determinant is rounded at the appropriate digit position to restore some or all of the

accuracy lost to floating-point arithmetic.

This refining technique can cause the computed determinant to exhibit discontinuity. To avoid

this, you can disable the refinement by setting flag –54.

Access: !Ø

OPERATIONS DET

( Ø is the left-shift of the 5key).

!´

NORMALIZE DET

( ´ is the left-shift of the Pkey).

Flags: Tiny Element (–54)

Input/Output:

Level 1/Argument 1 Level 1/Item 1

[[ matrix ]]

→

determinant

Example: For a square matrix A, the minor of element a

is the determinant of the submatrix that remains

after deleting row i and column j from the original matrix. Given a square matrix in level 3, i in

level 2, and j in level 1, the following program, MINOR determines the minor of the submatrix:

« → M row col

« M row ROW- DROP col COL- DROP DET »

For example, entering

[[ 1 2 3 ][ 4 5 6 ][ 7 8 9 ]] 2 3 MINOR

returns

-6