3) Let A be an n n matrix over F whose characteristic polynomial splits and...

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3) Let A be an n × n matrix over F whose characteristic polynomial splits and is given by: f(t) = det(A - tI) = (−1)"(t — λ1) († — λ2) ... († — λn) (we're not assuming that X's are distinct). (a) Show that det(A) = A₁ A2... An. 3) Let A be an n × n matrix over F whose characteristic polynomial splits and is given by: f(t) = det(A - tI) = (−1)"(t — λ1) († — λ2) ... († — λn) (we're not assuming that X's are distinct). (a) Show that det(A) = A₁ A2... An.

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To prove that detA we can use the fact that the characteristic poly... View the full answer