Linear algebra-how do I know if something is invertible?

[frasifrasi]

Linear algebra--how do I know if something is invertible?

Say I have a "reflection about the line y = x/3 in R^2," how do I know if the function or "T" is invertible?

Thank you.

 

[rootX]

T is inv if its matrix is invertible, I think reflecting about y = x/3 function/T is invertible .

just use vertical/horizontal line test for functions

 

[Dmak]

Well you could first find out what the matrix representation of this linear transformation is. Are you familiar with these terms?

 

[frasifrasi]

yes, but how does the vertical line test work?

 

[rootX]

I don't think it would work on transformations >>

for functions draw a vertical line, if it passes through the function twice then that means your function is not an actual function

and for inverse, draw horizontal line ...

something really simple stupid that I never used

 

[Dmak]

Well there is an invertible transformation for any reflection across a line through the origin.

 

[HallsofIvy]

Geometrically, if you reflect a second time across the same line, you are right back where you started. Any reflection is its own inverse.