In matrix $4 \times 4$ on the main diagonal I have elements $x + constant%$, where $x$ is real number. All other elements are the constans. How to prove that its determinant can be no-zero?
2026-04-03 22:26:54.1775255214
Determinant of a matrix with an unknown diagonal
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Hint : For determinant zero, we must have any row (column) say ist row must be scalar multiple of others. As you mentioned x is only on diagonal, so you cannot able to find suitable scalars which combination forms ist row. So determinant is not zero.