**22**
(Compute an inner product.)

**24**
(Compute the norm of a function in an inner product space.)

**28**
(Use Gram-Schmidt to produce an orthogonal basis for a function space.)
Use the mth309.function objects demonstrated in class.
Make a plot of your orthogonal basis functions.
I am **not** asking you to obtain expressions in terms of the original given basis.

**10.**
(Test if matrix is orthogonal.)

**22.**
(Orthogonally diagonalize a symmetric matrix.)

**26.**
(True or false. And justify.)

**40.**
(Orthogonally diagonalize a symmetric matrix:
A = Matrix([[8,2,2,-6,9],[2,8,2,-6,9],[2,2,8,-6,9],[-6,-6,-6,24,9],[9,9,9,9,-21]]) )
The eigenvalues are -30, 30, 15, 6 (with multiplicity 2).
Use mth309.nullbasis() to obtain an orthogonal basis for each eigenspace.
Caution: nullbasis() does not necessarily return an *orthogonal* basis for the nullspace.

**4.**
(Matrix of quadratic form.)

**16.**
(Classify quadratic form and obtain diagonal form.)

**22.**
(True or false. And justify.)