Jan 26 Inverses

Watch 3blue1brown video on inverses Tuesday office hours is extended by an hour

3.3 Inverses

• A linear transfrmation in ℝ² is equal to its inverse if equal to its own inverse.
• A square matrix A is invertible if there exists B such that AB = I_n.
• Give more examples of inverses we can figure out geometrically.
  • scaling
  • shear
• Properties of inverses. Assume A, B invertible, then
  • $(A^{-1}){-1} = A
  • (AB)^{-1}=B{-1}A^{-1}
  • If AC = AD then C = D.
• Derive method for computing. Explain both matrix multiplicatin version and linear map version.
• Do some basis examples.
• Give 2d formula