Question

Show that det(A) = 0 without directly evaluating the determinant. A = [-4 1 1 1 1; 1 -4 1 1 1; 1 1 -4 1 1; 1 1 1 -4 1; 1 1 1 1 -4]

Answer 1

You could interpret them as system of equation and answer the question easily

from A 

-4x + y + x + w =1

write in same form from A 

as this system has five variables and four of them are unknowns it means the unique solution is not possible 

So, det (A) = 0

Answer 2

Answer:You could interpret them as system of equation and answer the question easily

from A 

-4x + y + x + w =1

write in same form from A 

as this system has five variables and four of them are unknowns it means the unique solution is not possible 

So, det (A) = 0

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