A good answer might be:

(1, -3)T · (1, -3)T  =  (1)(1) + (-3)(-3)  =  1 + 9  =  10


Alway Positive

As with vectors, the dot product of a column matrix with itself will always be positive.

(x, y, z)T  · (x, y, z)T   =   x2 + y2 + z2   =   something zero or positive

No matter what x, y, and z are, their square is going to be zero or greater. So the sum is going to be zero or greater.

The only time the square of a real number is zero is when the real number is zero; so the only time the dot product of a column matrix with itself is zero is when it is the zero column matrix.

QUESTION 16:

g is a 3 dimensional vector. Solve the following equation for the elements of g:

g  ·  g =  0