1 Addition and subtraction

Matrices may be added if and only if they have the same dimension. They are then said to be conformable for addition. Each element in the first matrix is added to the corresponding element in the second matrix to form the same element in the solution.

$$\mbox{e.g.} \left( \begin{array}{rr} 1 & 4\ 2 & 5 \ 3 & 6... ...n{array}{rr} 9 & 15\ 11 & 17 \ 13 & 19 \end{array} \right)$$

or symbolically,

$${\bf A} + {\bf B} = {\bf C}.$$

One cannot add

$$\left( \begin{array}{rr} 1 & 4\ 2 & 5 \ 3 & 6 \end{array}... ... \left( \begin{array}{rr} 8 & 10\ 9 & 11 \end{array} \right)$$

because they have a different number of rows. Subtraction works in the same way as addition, e.g.

$$\left( \begin{array}{rr} 1 & 4\ 2 & 5 \ 3 & 6 \end{array} \... ...egin{array}{rr} -1 & -1\ 0 & 0 \ 1 & 1 \end{array} \right)$$

which is written

$${\bf A} - {\bf B} = {\bf C}.$$