Difference between revisions of "Addition of matrices"
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− | {{Navigation|before=[[The transpose of a matrix]]|overview=[[Matrices]]|next=[[Multiplication | + | {{Navigation|before=[[The transpose of a matrix]]|overview=[[Matrices]]|next=[[Multiplication of matrices]]}} |
+ | {{Exercise|Selftest: Addition of matrices}} | ||
+ | |||
+ | 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: | ||
− | |||
:<math> | :<math> | ||
\mathbf{A}+\mathbf{B}= | \mathbf{A}+\mathbf{B}= | ||
Line 8: | Line 10: | ||
a_{21} &\ddots & &\vdots\\ | a_{21} &\ddots & &\vdots\\ | ||
\vdots & & & \\ | \vdots & & & \\ | ||
− | a_{m1} & \dots & &a_{mn} | + | a_{m1} & \dots & & a_{mn} |
− | \end{ | + | \end{array}\right]+ |
− | \begin{ | + | \left[\begin{array}{cccc} |
b_{11} & b_{12} & \dots &b_{1n} \\ | b_{11} & b_{12} & \dots &b_{1n} \\ | ||
b_{21} &\ddots & &\vdots\\ | b_{21} &\ddots & &\vdots\\ | ||
\vdots & & & \\ | \vdots & & & \\ | ||
b_{m1} & \dots & &b_{mn} | b_{m1} & \dots & &b_{mn} | ||
− | \end{ | + | \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\\ | |
− | a_{11} & a_{ | ||
− | a_{ | ||
\vdots & & & \\ | \vdots & & & \\ | ||
− | a_{ | + | a_{m1}+b_{m1} & \dots & &a_{mn}+b_{mn} |
− | \end{ | + | \end{array}\right] |
</math> | </math> | ||
+ | |||
+ | {{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] | ||
+ | </math> | ||
+ | }} | ||
+ | |||
+ | [[Category:Article]] | ||
+ | [[Category:Matrices]] |
Latest revision as of 18:05, 13 November 2015
← Back: The transpose of a matrix | Overview: Matrices | Next: Multiplication of matrices → |
There are exercises as selftest for this article. |
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:
Example: Addition of two 3-by-3 matrices
|