I need help.

[norbertp86]

Can someone solve this for me please.... showing all the steps, please
UK’s general election took place in December 2019, and it was the first time young Ziutek cast his vote. Ziutek has been approached by his friend Dzesika, who is keen to learn who Ziutek has voted for. Ziutek decides to tell Dzesika – but not directly. He passes her the following numbers:

21 59 48 42 35 22
-9 -22 -15 -20 -5 -4

Dzesika also receives a Key to decrypt the message. Use the Key to find out Ziutek’s political affiliation:

Key: [tex]{2\space1 \choose -1 \space0}[/tex]
Taking A =1, B = 2, C =3 etc. decrypt the message and help Remus find out what Ziutek voted for.

question 14 on the paper

[Guest]

We are not told HOW to use the key but since it is a 2 by 2 matrix and the coded message consists of pairs of integers, I would try matrix multiplication.

[tex]\begin{pmatrix} 2 & 1 \\ -2 & 0 \end{pmatrix}\begin{pmatrix}21 \\ -9\end{pmatrix}=\begin{pmatrix} 33 \\ -42\end{pmatrix}[/tex].
Now, how do we interpret THAT? Well, at a guess, 33- 42= -9 and the 9th letter in the alphabet is I.

[tex]\begin{pmatrix} 2 & 1 \\ -2 & 0 \end{pmatrix}\begin{pmatrix}59 \\ -22\end{pmatrix}=\begin{pmatrix} 96 \\ -118\end{pmatrix}[/tex].
96- 118= -26 and the 26th letter is z.

[tex]\begin{pmatrix} 2 & 1 \\ -2 & 0 \end{pmatrix}\begin{pmatrix}48 \\ -15\end{pmatrix}=\begin{pmatrix} 81 \\ -96\end{pmatrix}[/tex].
81- 96= -15 and the 15th letter is o.

[tex]\begin{pmatrix} 2 & 1 \\ -2 & 0 \end{pmatrix}\begin{pmatrix}42 \\ -20\end{pmatrix}=\begin{pmatrix} 64 \\ -84\end{pmatrix}[/tex].
64- 84= -20 and the 20th letter is t.

[tex]\begin{pmatrix} 2 & 1 \\ -2 & 0 \end{pmatrix}\begin{pmatrix}35 \\ -5\end{pmatrix}=\begin{pmatrix} 65 \\ -70\end{pmatrix}[/tex].
65- 70= -5 and the 5th letter is e.

[tex]\begin{pmatrix} 2 & 1 \\ -2 & 0 \end{pmatrix}\begin{pmatrix}22 \\ -4\end{pmatrix}=\begin{pmatrix} 40 \\ -44\end{pmatrix}[/tex].
40- 44= -4 and the 4 letter is d.

Was there a candidate named "Izoted"?

I suspect that I screwed up on the second letter and she simply wrote "I voted"!