Difference between revisions of "Addition of matrices"

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     \vdots & & & \\
 
     \vdots & & & \\
 
     a_{m1}+b_{m1} & \dots & &a_{mn}+b_{mn}
 
     a_{m1}+b_{m1} & \dots & &a_{mn}+b_{mn}
 +
  \end{array}\right]
 +
</math><br/><br/>
 +
 +
{{Example
 +
|Title=Addition of two 3-by-3 matrices
 +
|Contents=<br/>
 +
:<math>
 +
\mathbf{A}_e+\mathbf{B}_e=
 +
  \left[\begin{array}{ccc}
 +
    1 & 3 & -2\\
 +
    0 & -1 & 3\\
 +
    2 & 4 & 2
 +
  \end{array}\right]+
 +
  \left[\begin{array}{ccc}
 +
    -3 & 2 & -1\\
 +
    2 & 4 & -3\\
 +
    0 & -2 & 1
 +
  \end{array}\right]=
 +
  \left[\begin{array}{ccc}
 +
    1-3 & 3+2 & -2-1\\
 +
    0+2 & -1+4 & 3-3\\
 +
    2+0 & 4-2 & 2-1
 +
  \end{array}\right]=
 +
  \left[\begin{array}{ccc}
 +
    -2 & 5 & -3\\
 +
    2 & 3 & 0\\
 +
    2 & 2 & 1
 
   \end{array}\right]
 
   \end{array}\right]
 
</math>
 
</math>
 +
}}

Revision as of 14:03, 16 May 2014

← Back: The transpose of a matrix Overview: Matrices Next: Multiplication with a vector →

Requirement for the addition of two matrices is, that they have the same number of rows and the same number of colums. So both matrices have to be an m-by-n matrix. The addition is made by adding each the components:

\mathbf{A}+\mathbf{B}= \left[\begin{array}{cccc} a_{11} & a_{12} & \dots &a_{1n} \\ a_{21} &\ddots & &\vdots\\ \vdots & & & \\ a_{m1} & \dots & & a_{mn} \end{array}\right]+ \left[\begin{array}{cccc} b_{11} & b_{12} & \dots &b_{1n} \\ b_{21} &\ddots & &\vdots\\ \vdots & & & \\ b_{m1} & \dots & &b_{mn} \end{array}\right]= \left[\begin{array}{cccc} a_{11}+b_{11} & a_{12}+b_{12} & \dots &a_{1n}+b_{1n} \\ a_{21}+b_{21} &\ddots & &\vdots\\ \vdots & & & \\ a_{m1}+b_{m1} & \dots & &a_{mn}+b_{mn} \end{array}\right]

Example: Addition of two 3-by-3 matrices


\mathbf{A}_e+\mathbf{B}_e= \left[\begin{array}{ccc} 1 & 3 & -2\\ 0 & -1 & 3\\ 2 & 4 & 2 \end{array}\right]+ \left[\begin{array}{ccc} -3 & 2 & -1\\ 2 & 4 & -3\\ 0 & -2 & 1 \end{array}\right]= \left[\begin{array}{ccc} 1-3 & 3+2 & -2-1\\ 0+2 & -1+4 & 3-3\\ 2+0 & 4-2 & 2-1 \end{array}\right]= \left[\begin{array}{ccc} -2 & 5 & -3\\ 2 & 3 & 0\\ 2 & 2 & 1 \end{array}\right]
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