Maintenance script: Initial automated import

2016-02-24T18:40:20Z

Initial automated import

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{{Template:TI-BASIC:Command
|picture=INVERSE.GIF
|summary=Returns the reciprocal of a number (1 divided by the number). For matrices, finds the matrix inverse.
|syntax=''value''ֿ¹
|location=Press [''x''ֿ¹]
|compatibility=TI-83/84/+/SE
|size=1 byte
}}

The ֿ¹ command returns the reciprocal of a number, equivalent to dividing 1 by the number (although reciprocals are sometimes more convenient to type). It also works for lists, by calculating the reciprocal of each element.

The ֿ¹ command can also be used on matrices, but it is the matrix inverse that is computed, not the reciprocal of each element. If [A] is an N by N (square) matrix, then [A]ֿ¹ is the N by N matrix such that [A][A]ֿ¹=[A]ֿ¹[A] is the identity matrix. ֿ¹ does not work on non-square matrices.

4ֿ¹
.25
{1,2,3}ֿ¹
{1 .5 .3333333333}
[[3,2][4,3]]ֿ¹
[[3 -2]
[-4 3 ]]

Much like the number 0 does not have a reciprocal, some square matrices do not have inverses (they are called singular matrices) and you'll get an error when you try to invert them.

= Optimization =

Writing Aֿ¹B instead of B/A is sometimes beneficial when B is a complicated expression, because it allows you to take off closing parentheses of B. For example:

:(P+√(P²-4Q))/2
can be
:2ֿ¹(P+√(P²-4Q

This may be slower than dividing. There are also situations in which this optimization might lose precision, especially when the number being divided is large:

7fPart(4292/7
1
7fPart(7ֿ¹4292
.9999999999

= Error Conditions =

* '''[[TI-BASIC:Errors#divideby0|ERR:DIVIDE BY 0]]''' is thrown when trying to take the reciprocal of 0.
* '''[[TI-BASIC:Errors#singularmat|ERR:SINGULAR MAT]]''' is thrown when trying to invert a singular matrix.

= Related Commands =

* [[TI-BASIC:2|²]]
* [[TI-BASIC:3|³]][[Category:TI-BASIC]]
[[Category:TIBD]]

TI-BASIC:Inverse - Revision history

Maintenance script: Initial automated import