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Jan 26 Inverses

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

3.3 Inverses

• A linear transfrmation in $\mathbb{R}^2$ 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