Consider the n x n matrix with all zeros except for the real numbers α1 ... αn on the diagonal. Prove, by checking that it preserve addition and scalar multiplication, that this matrix corresponds to a linear transformation of R^n

That a1 and an are alpha-1 and alpha-n.

I really hope this question makes sense to someone. I'm not the strongest at math and I need this course to get into a Master's program. I really hope you can help me!

Thanks so much!

- H.

Edit: I posted this in another form area by accident, and I hope it's ok if I reposted it here. :/