Thread: Consider this matrix and prove...

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. :/

Originally Posted by hyrule

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. :/

That an operator is a linear transformation on means:



for any and in and and in

Here means your matrix is , is a (column) vector in and denote the matrix prioduct of and .

Now what have you tried, and what problems are you having?

CB

I haven't tried too much with this question because I am just stumped at this entire question. I know about transformation matrices and all that, but I wondered if I was supposed to multiply the matrix n x n by x1, x2, x3? I'm just not very strong in this type of math, heh.

Originally Posted by hyrule

I haven't tried too much with this question because I am just stumped at this entire question. I know about transformation matrices and all that, but I wondered if I was supposed to multiply the matrix n x n by x1, x2, x3? I'm just not very strong in this type of math, heh.

Because your matrix is diagonal



CB

Oooh ok, I get it. So because I have alpha-n number of all real numbers in the diagonal matrix, I needed to multiply it with Xn number of variables.

I had a suspiscian that I would have to multiply by x variables, but I just wasn't confident in my own answer. You've really helped me understand it better, thank you!!