(Efomm 2017) Calcule o determinante da matriz A de
(Efomm 2017) Calcule o determinante da matriz A de ordem n:
\( A=\begin{pmatrix} 1 & 1 & 1 & 1 & 1 &\cdots & 1\\ 1 & 3 & 1 & 1 & 1 &\cdots & 1\\ 1 & 1 & 5 & 1 & 1 &\cdots & 1\\ 1 & 1 & 1 & 7 & 1 &\cdots & 1\\ 1 & 1 & 1 & 1 & 9 &\cdots & 1\\ \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots\\ 1 & 1 & 1 & 1 & 1 &\dots & 2n-1 \end{pmatrix}\)
A
\(\large \det A=\prod_{k=1}^{n-1}2k\)
B
\(\large\large \det A=\prod_{k=1}^{n-1}(2k-1)\)
C
\(\large\large \det A=\prod_{k=1}^{n-1}2^k\)
D
\(\large\large \det A=\prod_{k=1}^{n-1}2^{k-1}\)
E
1
