Answer:
(1, -3)T · (1, -3)T = (1)(1) + (-3)(-3) = 1 + 9 = 10
(1, -3)T · (1, -3)T = (1)(1) + (-3)(-3) = 1 + 9 = 10
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.
g is a 3 dimensional vector. Solve the following equation for the elements of g:
g · g = 0