What do you suppose is the length of the vector represented by:

(3, 0)^{T}

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.

Vector **a**
(the blue vector in the diagram)
is aligned with the y axis.
Its matrix is **(0,4) ^{T}**