Theory of Intelligence
11TH•Mathematics•Matrices And Determinants•Question 8

Solution

The point $A$ is mapped to $(30,20,-5)$ by the scaling matrix $P=\begin{bmatrix}-5&0&0\\0&-5&0\\0&0&-5\end{bmatrix}$. Find the coordinates of $A$.

timer2 min read•forumLesson Discussion

Solution

Given scaling matrix:

P=[−5000−5000−5]P=\begin{bmatrix}-5&0&0\\0&-5&0\\0&0&-5\end{bmatrix}

and AA is mapped to A′=(30,20,−5)A'=(30,20,-5).

Using the hint:

PA=A′PA=A'

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

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

So:

x=−6,y=−4,z=1x=-6,\quad y=-4,\quad z=1 A=(−6,−4,1)\boxed{A=(-6,-4,1)}

Discuss theoretical concepts, mathematical formulas, and architectural foundations.

Supports inline code with `backticks`
No comments yet. Be the first to start the discussion!
arrow_back
Previous Question
Question 7
Next Question
Question 9
arrow_forward