Does the following matrix have an inverse?

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

    I used this theorem: N N-1 = In

    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
     
  2. jcsd
  3. Hurkyl

    Hurkyl 16,090
    Staff Emeritus
    Science Advisor
    Gold Member

    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.
     
  4. 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.
     
  5. 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.
     
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