Jadzia
  • Jadzia
Quick Question: When is a matrix not invertible? can you give me an example please?
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
if determinant of a matrix is zero,then it is not invertible.
Jadzia
  • Jadzia
even though it is an nxn matrix? for example.. |dw:1449194815844:dw| so matrix A is not invertible?
jim_thompson5910
  • jim_thompson5910
@Jadzia the bottom row is all 0, so the determinant will be 0. That means A is not invertible. You are correct. another example would be to have row3 equal to some linear combination of rows 1 and 2. Eg: R3 = R1+R2. That leads to another matrix with determinant 0

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Jadzia
  • Jadzia
oh i see.. one more thing.. can mxn (if m is not equal to n) matrix also be invertible?
jim_thompson5910
  • jim_thompson5910
no, the matrix must be square (ie, m = n) for it to be invertible
Jadzia
  • Jadzia
okay, that's all i wanted to confirm. Thank you so much ^_^
jim_thompson5910
  • jim_thompson5910
you're welcome
anonymous
  • anonymous
\[A A ^{-1}=I\] \[if~m \neq n,~then~what~about~order~of~I ?\]
anonymous
  • anonymous
so it should be a square matrix.
Jadzia
  • Jadzia
oh that makes so much sense :o
Jadzia
  • Jadzia
thanks again :D

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