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 $$.

$$.