Selftest: Matrix multiplication with a scalar

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Exercises for chapter Matrices | Article: Multiplication with a scalar

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1. Is there any scalar constant $c$, so that the following equation holds?

$\left[\begin{array}{ccc}1&2&3\\0&2&1\\2&3&0\end{array}\right]\cdot c = \left[\begin{array}{ccc}2&4&6\\0&4&2\\3&6&0\end{array}\right]$

	$c=0.5$
	$c=1$
	$c=2$
	There is no $c$
→	$c=2$ would be correct for all the green colored components in the result matrix: $\left[\begin{array}{ccc}{\color{Green}2}&{\color{Green}4}&{\color{Green}6}\\{\color{Green}0}&{\color{Green}4}&{\color{Green}2}\\{\color{Red}3}&{\color{Green}6}&{\color{Green}0}\end{array}\right]$. For the red component $c=1.5$ would be right. So there is no general $c$, that holds for all the components.

2. Is there any scalar constant $c$, so that the following equation holds?

$\left[\begin{array}{ccc}2&0&1\\0&2&3\\1&1&0\end{array}\right]\cdot c = \left[\begin{array}{ccc}4&0&2\\0&4&6\\2&2&0\end{array}\right]$

	$c=0.5$
	$c=1$
	$c=2$
	There is no $c$
→	If all the components of the left matrix are multiplied by $c=2$, it results in the right matrix.

3. Fill in the correct values of the resulting matrix:

$\left[\begin{array}{ccc}3&2&1\\2&1&2\\2&3&1\end{array}\right]\cdot 3 =$

4. Is the following equation correct?

$\left[\begin{array}{ccc}2&0&1\\4&1&3\\2&2&1\end{array}\right]\cdot 3 = \left[\begin{array}{ccc}6&0&3\\12&2&9\\6&6&3\end{array}\right]$

	Yes
	No
→	The central component in the resulting matrix is $2$. But it has to be $3$. So the equation is not correct.

5. Is the following equation correct?

$\left[\begin{array}{ccc}1&0&2\\2&1&3\\3&2&1\end{array}\right]\cdot 2 = \left[\begin{array}{ccc}2&0&4\\4&2&6\\6&4&2\end{array}\right]$

	Yes
	No
→	The multiplication holds for each of the components.

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