(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

find all real values of k for which A is diagonalizable.

A = [ 1 1 ]

[ 0 k ]

3. The attempt at a solution

let L = lamba = eigenvalue

I did this:

det(A - LI) = L^{2}- Lk - L + k

so then it sorta looks like a quadratic so I did this:

L^{2}- Lk - L + k = 0

L^{2}- L(k+1) + k = 0

and used the quadratic equation

x = (-b +- sqrt(b^{2}-4ac)) / 2a

so then I got stuck at this point:

((k+1) +- (k-1)) / 2

and this is where I got really really stuck. I'm not sure how or what to conclude about matrix A being diagonalizable for all real values of k.

or can I skip the quadratic equation method and just do this instead?

(1-L)(k-L) = 0

then

L = 1 and L = k

so then matrix A is diagonalizable for any real number k except 0?

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# Homework Help: Find all real values of k for which A is diagonalizable

**Physics Forums | Science Articles, Homework Help, Discussion**