Question

Construct a matrix that triples the height, width, and length of an objective in 3D

Answer 1

`A=\left[\begin{array}{ccc}3&0&0\\0&3&0\\0&0&3\end{array}\right]`

Explanation:

Our dimension vector is:

`v=\left[\begin{array}{c}x\\y\\z\end{array}\right]`

We need a matrix that returns another 3x1 vector, where only each component is 3 times the original value.

Let's see for x:

`X=A*\left[\begin{array}{c}x\\y\\z\end{array}\right]`

if
`A=\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right]`

then:

a*x+b*y+c*z=3*x then, b=c=0 and a=3

d*x+e*y+f*z=3*y then, d,f=0 and e=3

g*x+h*y+i*z=3*z then g,h=0 and i=3