Extra Pure

Question 1

What eigenvalues do reflections have?

Answer 1

1 is the direction of the mirror line

-1 is the direction of the normal line

Question 2

What is the trace of a matrix?

Answer 2

for matrix (a, b, c, d), the trace of the matrix is (a + d)

trace of matrix = sum of eigenvalues

Question 3

how do you find a vector that’s normal to the surface g(x, y, z) = 0

Answer 3

grad(g) at a point on the surface

Question 4

what is the Latin square property?

Answer 4

a table where each member of the group only appears once in each row and column

Question 5

what is a SYMMETRY GROUP?

Answer 5

for a geometric object, it’s the group of all transformations that map the object to itself

Question 6

how can you tell if a group is Abelian from a Cayley table?

Answer 6

the table is symmetrical about the leading diagonal

Question 7

what is the equivalent of a point of inflection in 3D?

Answer 7

a ‘saddle point’ : z increases in some directions from the saddle and decreases at other points