How do you subtract column vectors?

When subtracting column vectors, the operation is performed component-wise. This means that you take each corresponding element from the two vectors and subtract the elements from one another.

So, if you have two column vectors, for example:

[ \mathbf{v_1} = \begin{pmatrix} a \ b \end{pmatrix} ]

and

[ \mathbf{v_2} = \begin{pmatrix} c \ d \end{pmatrix} ]

the subtraction would be carried out as follows:

[ \mathbf{v_1} - \mathbf{v_2} = \begin{pmatrix} a - c \ b - d \end{pmatrix} ]

This is consistent with the choice that suggests subtracting the values in the same row from each other, which means you subtract the corresponding values directly, keeping the calculation organized in terms of their respective position in the vector.

This method is necessary because columns in vectors represent individual components. Therefore, subtracting them requires referring to the correct position for both the top and bottom elements, confirming that you are accurately addressing the respective values in the vectors.