1. Find the standard matrix of .
  2. Find the standard matrix of if rotates a point in clockwise through 180° and then reflects the point about the x-axis.
  3. For , compute
  4. Forr , compute

    5. a) b) c)

     

     

  5. Suppose is invertible. Solve each of the following for .

    6. a) b)

     

  6. Given that , write as the product of elementary matrices.

    7.  

  7. Write the inverse of each of the following elementary matrices.

    8. a) b)

    c)

     

     

     

  8. Find the inverse of . Please show your work.

    9.  

     

  9. Find an LU decomposition for
. You may want to refer to the previous problem.

 

 

  1. For
.

( You may want to refer to one of the previous 2 problems.)

11. For , a) find a basis for the column space of

  1. find a basis for the null space of

 

 

12. If is 3x5, find minimum and maximum values for the dimension of the null space of .

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