Difference between revisions of "Multiplication with a scalar"
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{{Navigation|before=[[Matrices]]|overview=[[Matrices]]|next=[[The transpose of a matrix]]}} | {{Navigation|before=[[Matrices]]|overview=[[Matrices]]|next=[[The transpose of a matrix]]}} | ||
+ | {{Exercise|Selftest: Matrix multiplication with a scalar}} | ||
− | A matrix is multiplied with a scalar by multiplying all the components with the scalar:<br/><br/> | + | A matrix is multiplied with a scalar by multiplying all the components with the scalar. The result is again a matrix with the same dimensions:<br/><br/> |
:<math> | :<math> | ||
+ | \mathbf{A} \cdot c =c \cdot \mathbf{A}=c\cdot\left[ | ||
+ | \begin{array}{ccc} | ||
+ | a_{11} & a_{12} & a_{13}\\ | ||
+ | a_{21} & a_{22} & a_{23}\\ | ||
+ | a_{31} & a_{32} & a_{33} | ||
+ | \end{array}\right]= | ||
+ | \left[\begin{array}{ccc} | ||
+ | c\cdot a_{11} & c\cdot a_{12} & c\cdot a_{13}\\ | ||
+ | c\cdot a_{21} & c\cdot a_{22} & c\cdot a_{23}\\ | ||
+ | c\cdot a_{31} & c\cdot a_{32} & c\cdot a_{33} | ||
+ | \end{array}\right] | ||
+ | </math> | ||
− | </math> | + | {{Example |
+ | |Title=Multiplying a matrix with a scalar | ||
+ | |Contents=<br/> | ||
+ | :<math>\begin{align} | ||
+ | \mathbf{A}&=\left[ | ||
+ | \begin{array}{ccc} | ||
+ | 2 & 3 & 0\\ | ||
+ | 4 & 1 & 2\\ | ||
+ | 3 & 1 & 4 | ||
+ | \end{array}\right],\quad c=3\\ | ||
+ | c \cdot\mathbf{A}&=3\cdot\left[\begin{array}{ccc} | ||
+ | 2 & 3 & 0\\ | ||
+ | 4 & 1 & 2\\ | ||
+ | 3 & 1 & 4 | ||
+ | \end{array}\right]= | ||
+ | \left[\begin{array}{ccc} | ||
+ | 3\cdot 2 & 3\cdot 3 & 3\cdot 0\\ | ||
+ | 3\cdot 4 & 3\cdot 1 & 3\cdot 2\\ | ||
+ | 3\cdot 3 & 3\cdot 1 & 3\cdot 4 | ||
+ | \end{array}\right]= | ||
+ | \left[\begin{array}{ccc} | ||
+ | 6 & 9 & 0\\ | ||
+ | 12 & 3 & 6\\ | ||
+ | 9 & 3 & 12 | ||
+ | \end{array}\right] | ||
+ | \end{align}</math> | ||
+ | }} | ||
+ | |||
+ | [[Category:Article]] | ||
+ | [[Category:Matrices]] |
Latest revision as of 18:03, 13 November 2015
← Back: Matrices | Overview: Matrices | Next: The transpose of a matrix → |
There are exercises as selftest for this article. |
A matrix is multiplied with a scalar by multiplying all the components with the scalar. The result is again a matrix with the same dimensions:
Example: Multiplying a matrix with a scalar
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