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]

Question

Madeleine Carney

Mathematics

3 September, 11:36

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]

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Answers (1)

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Boston Simmons · 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