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I have a $2 \times 2$ matrix $$ A= \left( \begin{array}{cc} 4 & 10 \\ 16 & 24 \end{array} \right). $$ If I was to divide this matrix by $2$, do I just perform division on each number giving $$ \frac{A}{2}= \left( \begin{array}{cc} 2 & 5 \\ 8 & 12 \end{array} \right), $$ or is this wrong?

Thanks in advance!

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  • $\begingroup$ Yes. Your procedure is correct. $\endgroup$ Nov 14, 2015 at 20:46

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In general, matrices do not work like "regular" numbers. What you mean to write is $$\big(\frac{1}{2}\big)A = \begin{bmatrix} 2 & 5 \\ 8 & 12 \\ \end{bmatrix}$$ Although it may seem like the same thing, as $A/2$, the notation means something. Matrices, typically, have different properties in terms of inverses than the $1 \times 1$ matrices--we can think of any scaler as a $1\times1$ matrix. If you would like to read more about this, https://en.wikipedia.org/wiki/Matrix_(mathematics).

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  • $\begingroup$ Okay thanks, I'm aware they don't work like regular numbers through multiplication and such. However I was given a matrix called B and had to figure out B/2. Link was helpful also. $\endgroup$ Nov 14, 2015 at 20:46
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    $\begingroup$ I wouldn't be so strict about notation, I've seen OP's way of writing it countless times. $\endgroup$ Nov 14, 2015 at 20:47
  • $\begingroup$ @BlakeBit I am glad the link helped. I wouldn't worry about it too much if you are outside the mathematics departments! But all-in-all, yes; you just divide each entry by one half. $\endgroup$
    – 9301293
    Nov 14, 2015 at 20:48

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