What do you suppose is the length of the vector represented by:
It seems plausible that the length is 3 units.
When a 2D vector is aligned with the x axis, the column matrix that represents it has a non-zero value in the first element, and zero for the second element.
The green vector is represented by: (3, 0)T. It is easy to determine its length — the length is the value of the single non-zero element.
(the blue vector in the diagram)
is aligned with the y axis.
Its matrix is