# Addition of Matrices

## Key Questions

• A matrix is a table of numbers (or other elements) disposed in rows ans columns.
For example:
$A =$$\left(\begin{matrix}1 & 2 & 3 \\ 3 & 4 & 6\end{matrix}\right)$
This is a rectangular matrix called $A$ with $2$ rows and $3$ columns, so you say thart $A$ has order $2 \times 3$ (2 by 3).

You can have square matrices when the numbers of rows is equal to the number of columns:
$B =$$\left(\begin{matrix}1 & 2 & 3 \\ 3 & 4 & 6 \\ 3 & 2 & 1\end{matrix}\right)$
Where $B$ is a square matrix od order $3 \times 3$ or simply $3$.

You can also have matrices with one column only or one row only :
$C =$$\left(\begin{matrix}1 \\ 6 \\ 7\end{matrix}\right)$ or $D =$$\left(\left(1 , 2 , 3 , 4 , 6\right)\right)$
these are sometimes called vectors or column vector and row vector.

A bank statement is an example of a matrix:

• You add the corresponding elements to get your result.

This is one of the easier matrix operations. Here is an example:

[a b c]+[g h i] = [a+g, b+h, c+i]
[d e f].. [j k l] ... [d+j,. e+k,. f+l]

Ignore the "."; it's the only way to space things right now.

Since we are adding corresponding elements, the matrices must have the same dimensions; the answer must also have the same dimension.

• The 4x4 matrix :

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

and this one

1 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

are equivalent, because they are both of rank 1.

Actually : two nxp matrices A and B are equivalents iff rank(A) = rank(B).

NB. rank(A) is the dimension of space engendered by the columns of A.

• This key question hasn't been answered yet.

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