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Just a quick question, how does the (-2, 3) matrix become (-4 6) when its added to the other matrix.

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Thanks for any help Regards Mike

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You have:

$$-\frac{1}{2}\begin{pmatrix} 3-2\sqrt{3} \\ 2+3\sqrt{3} \end{pmatrix} + \begin{pmatrix} -2 \\ 3 \end{pmatrix}$$

This can be factorised.

$$\frac{1}{2}\begin{pmatrix} -(3-2\sqrt{3}) \\ -(2+3\sqrt{3}) \end{pmatrix} + \frac{1}{2} \begin{pmatrix} -4 \\ 6 \end{pmatrix}$$

What we did is we multiplied each entry in the matrix on the right by $2$ to compensate for the multiplication by $\frac{1}{2}$

Thus, we may now add them (combine the matrices).

$$\frac{1}{2}\begin{pmatrix} -3+2\sqrt{3}-4 \\ -2-3\sqrt{3}+6 \end{pmatrix}$$

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    Hi, Thanks for the reply. I didnt think the 1/2 was multiplying the second matrix only the first? – 2017-01-10
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    Yes, it was multiplying only the 1st matrix. So what we did was we factorised the 2nd matrix to get it into the form of the 1st. – 2017-01-10
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    I get it now. When the matrices have combined you've had to multiply by 2 to compensate the for 1/2. Thanks – 2017-01-10
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    Hi, I cant see a checkbox – 2017-01-10