Difference between revisions of "Selftest: Matrix multiplication with a scalar"
From Robotics
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||<math>c=2</math> would be correct for all the green colored components in the result matrix: <math>\left[\begin{array}{ccc}{\color{Green}2}&{\color{Green}4}&{\color{Green}6}\\{\color{Green}0}&{\color{Green}4}&{\color{Green}2}\\{\color{Red}3}&{\color{Green}6}&{\color{Green}0}\end{array}\right]</math>. For the red component <math>c=1.5</math> would be right. So there is no general <math>c</math>, that holds for all the components. | ||<math>c=2</math> would be correct for all the green colored components in the result matrix: <math>\left[\begin{array}{ccc}{\color{Green}2}&{\color{Green}4}&{\color{Green}6}\\{\color{Green}0}&{\color{Green}4}&{\color{Green}2}\\{\color{Red}3}&{\color{Green}6}&{\color{Green}0}\end{array}\right]</math>. For the red component <math>c=1.5</math> would be right. So there is no general <math>c</math>, that holds for all the components. | ||
− | |||
{'''Is there any scalar constant <math>c</math>, so that the following equation holds?'''<br/> | {'''Is there any scalar constant <math>c</math>, so that the following equation holds?'''<br/> | ||
:<math> | :<math> | ||
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+ No | + No | ||
||The central component in the resulting matrix is <math>2</math>. But it has to be <math>3</math>. So the equation is not correct. | ||The central component in the resulting matrix is <math>2</math>. But it has to be <math>3</math>. So the equation is not correct. | ||
+ | |||
+ | {'''Is the following equation correct?'''<br/> | ||
+ | :<math> | ||
+ | \left[\begin{array}{ccc}1&0&2\\2&1&3\\3&2&1\end{array}\right]\cdot 2 = \left[\begin{array}{ccc}2&0&4\\4&2&6\\6&4&2\end{array}\right] | ||
+ | </math><br/> | ||
+ | | typ="()" } | ||
+ | + Yes | ||
+ | - No | ||
+ | ||The multiplication holds for each of the components. | ||
</quiz> | </quiz> |
Revision as of 16:23, 18 June 2014
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