Linear transformation across a plane

[desert saffron]

Can someone please help explain this question? Find the transformation matrix of the reflection about the plane 𝑥−𝑦+𝑧=0

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[sacred crystal]

Have you done Eigenvectors?

[desert saffron]

not quite

but they didn't teach it with that in mind

[sacred crystal]

Right

For a reflection in a plane you can just work out the matrix by mapping vectors

The normal vector must map to its negative version

And then two vectors in the plane map to themselves

Set up some simulations equations and it should solve

[desert saffron]

I get that bit

could you write it out by any chance?

@sacred crystal

[sacred crystal]

Ye one sec

[desert saffron]

ty ty

[desert saffron]

oh right yeah because the vectors in the actual plane will just map to themselves

lemme try it

Doesn't look to be right tho

@sacred crystal

[sacred crystal]

What do you get

[sacred crystal]

Somethings gone wrong in your algebra

I lost a negative sign one second

[desert saffron]

I used a calculator

[sacred crystal]

I’ve seen it I hade a mistake mb

[desert saffron]

I used these 2 vectors and I got it

tysm

[sacred crystal]

Sweet

Yes sorry I got that last vector y and z the wrong way round glad it worked tho