Determinant of a general Matrix

Asked Aug 23 '17 at 23:40

Active Aug 23 '17 at 23:40

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What are the steps to solve for the Determinant of this Matrix? I thought about turning it into a lower triangular Matrix, but I can't figure how.

Thanks in advance.

Let $A = $ $\begin{pmatrix}1 & 1& 1 & \cdots & 1 \\ 1 & 1+a2 & 1 & \cdots & 1 \\ 1 & 1& 1 + a3 &\cdots & 1 \\ \cdots & \cdots & \cdots & \cdots & \cdots \\ 1& 1 & 1 &\cdots& 1 + an \end{pmatrix}$

asked Aug 23 '17 at 23:40

Leon Held

5

Hint : Subtract the first row from every other row. You immediately see that $D=a_2\cdot a_3\cdots a_n$ – Peter Aug 23 '17 at 23:53
Neither the close-vote nor the downvote are justified since in the question, the key idea is mentioned. – Peter Aug 24 '17 at 00:06
1

I love you so much. Thanks for the clarification. – Leon Held Aug 24 '17 at 00:07
I use an alternate (but not necessarily better) approach on a similar question here. – Ben Grossmann Aug 24 '17 at 00:35
Possible duplicate of Determinant of rank-one perturbation of a diagonal matrix – hardmath Aug 24 '17 at 04:54

Determinant of a general Matrix

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