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. The result is again a matrix:<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> | ||
− | c \cdot \mathbf{A}=c\cdot\left[ | + | \mathbf{A} \cdot c =c \cdot \mathbf{A}=c\cdot\left[ |
\begin{array}{ccc} | \begin{array}{ccc} | ||
a_{11} & a_{12} & a_{13}\\ | a_{11} & a_{12} & a_{13}\\ | ||
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{{Example | {{Example | ||
|Title=Multiplying a matrix with a scalar | |Title=Multiplying a matrix with a scalar | ||
− | |Contents= | + | |Contents=<br/> |
:<math>\begin{align} | :<math>\begin{align} | ||
\mathbf{A}&=\left[ | \mathbf{A}&=\left[ | ||
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4 & 1 & 2\\ | 4 & 1 & 2\\ | ||
3 & 1 & 4 | 3 & 1 & 4 | ||
− | \end{array}\right] | + | \end{array}\right]= |
\left[\begin{array}{ccc} | \left[\begin{array}{ccc} | ||
3\cdot 2 & 3\cdot 3 & 3\cdot 0\\ | 3\cdot 2 & 3\cdot 3 & 3\cdot 0\\ | ||
3\cdot 4 & 3\cdot 1 & 3\cdot 2\\ | 3\cdot 4 & 3\cdot 1 & 3\cdot 2\\ | ||
3\cdot 3 & 3\cdot 1 & 3\cdot 4 | 3\cdot 3 & 3\cdot 1 & 3\cdot 4 | ||
− | \end{array}\right] | + | \end{array}\right]= |
\left[\begin{array}{ccc} | \left[\begin{array}{ccc} | ||
6 & 9 & 0\\ | 6 & 9 & 0\\ | ||
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\end{align}</math> | \end{align}</math> | ||
}} | }} | ||
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+ | [[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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