A vector is first rotated by displaystyle{90}^{circ} along x-axis and then scaled up by 5 times is equal to displaystyle{left({15},-{10},{20}right)}. What was the original vector

Let us consider the vector (x, y, z).
The vector is first rotated by ${\displaystyle {90}^{\circ }}$ along x - axis and then scaled up by 5 times.
Ratation: In homogeneous coordinates, the matrix for a rotetion about the origin through a given angle ${\displaystyle \theta isB=\left[\begin{array}{ccc}\cos \theta & -\sin \theta & 0\\ \sin \theta & \cos \theta & 0\\ 0& 0& 1\end{array}\right]}$
The vector (x, y, z) is rotated by ${\displaystyle {90}^{\circ }}$ along x-axis then the vector becomes
${\displaystyle \left[\begin{array}{c}\cos {90}^{\circ }-\sin {90}^{\circ }0\\ \sin {90}^{\circ }\cos {90}^{\circ }\\ 001\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]}$
${\displaystyle =\left[\begin{array}{c}0-10\\ 100\\ 001\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]}$
${\displaystyle =\left[\begin{array}{c}-y\\ x\\ z\end{array}\right]}$
Now, the vector is scaled up by 5 times.
Scaling: In homogeneous coordinates, a scaling about the origin with scale factors c in the x-direction and c in the y-direction is computed by multiplying the vector by the matrix
${\displaystyle A=\left[\begin{array}{c}c00\\ 0c0\\ 001\end{array}\right]}$
Thus, the vector becomes
${\displaystyle \left[\begin{array}{c}500\\ 050\\ 001\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]}$
${\displaystyle =\left[\begin{array}{c}-5y\\ 5x\\ z\end{array}\right]}$
Now, given that the reduced vector is ${\displaystyle (15,-10,20)}$. Therefore, we have
${\displaystyle \left[\begin{array}{c}-5y\\ 5x\\ z\end{array}\right]=\left[\begin{array}{c}15\\ -10\\ 20\end{array}\right]}$
By the equality of two matrices we have
${\displaystyle \{\begin{array}{c}-5y=15\\ 5x=-10\\ z=20\end{array}=\{\begin{array}{c}y=-3\\ x=-2\\ z=20\end{array}}$
Thus, the original vector is (-2, -3, 20)