Proving χA(x) = x^2 -tr(A)x + det(A) for Matrix A in Linear Algebra Homework

Chewybakas
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Homework Statement



Let A ε M2x2 prove χA(x) = x^2 -tr(A)x + det(A)


Homework Equations





The Attempt at a Solution


Hi all, this is an assignment equation and the right hand side i can perfectly understand but i can't understand the left hand side, What is it i am looking for?? Can anyone help?
 
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Chewybakas said:

Homework Statement



Let A ε M2x2 prove χA(x) = x^2 -tr(A)x + det(A)


Homework Equations





The Attempt at a Solution


Hi all, this is an assignment equation and the right hand side i can perfectly understand but i can't understand the left hand side, What is it i am looking for?? Can anyone help?

The left side looks like it is supposed to be the characteristic polynomial of A.
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...
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