First Principles AI

Accedmychevron_right11thchevron_rightmathchevron_rightMatrices And Determinantschevron_rightExercise 4.3

Solution

Given scaling matrix:

P=\begin{bmatrix}-5&0&0\\0&-5&0\\0&0&-5\end{bmatrix}

and $A$ is mapped to $A'=(30,20,-5)$ .

Using the hint:

PA=A'

Let $A=(x,y,z)$ . Then:

(-5x,-5y,-5z)=(30,20,-5)

So:

x=-6,\quad y=-4,\quad z=1

\boxed{A=(-6,-4,1)}