Compute the maximum and minimum values attained by the quadratic form , where
subject to the constraint , and determine a unit vector where each extremum is
attained.

**Maximum = ** 6 is attained at

**Minimum = ** -4 is attained at

Find the maximum value for the quadratic form corresponding to the matrix and
the vector you computed above, subject to and .

**Maximum = ** -4 is attained at

Find the maximum value for the quadratic form:

, subject to .

**Maximum = ** .

Given the orthogonal diagonalization of below:
,

Find the unit vector at which the quadratic form attains its maximum subject to .
Then find the unit vector at which attains its maximum subject to both and
.

.