Does the following matrix have an inverse?

[frankR]

N= [i,1;-1,i]

I used this theorem: N N^-1 = I_n

Thus:

[i,1;-1,i]*[a,b:c,d]=[1,1;1,1]

I then found:

ia+c=1
ib+d=1
-a+ic=1
-b+id=1

Can I conclude an inverse does not exist. If so, how?

If not, what do I do?


Thanks,

Frank

 

[Hurkyl]

I₂ = [1, 0; 0, 1]


What theorems have you learned about invertible matrices? (e.g. have you learned anything about how to tell if a matrix is invertible based on its determinant)


Or, you could apply the algorithm for computing inverses and see if you get an answer or if its impossible.

 

[frankR]

Originally posted by Hurkyl


Or, you could apply the algorithm for computing inverses and see if you get an answer or if its impossible.

I just found this:

N^-1 exists only if:

det(NN^-1 != 0

I'm a little rusty on my linear algebra, plus I got a concusion yesterday.

 

[arcnets]

frankR,
Hurkyl has told you what I₂ is, because you got that wrong. Just redo your calculation using Hurkyl's hint and you should be able to answer this easily.