Mathematics · 2019
JEE Main · 9 April 2019, Shift 1 · Q65
If [1, 1; 0, 1] · [1, 2; 0, 1] · [1, 3; 0, 1] · … … ….. [1, n-1; 0, 1] = [1, 78; 0, 1], then the inverse of [1, n; 0, 1] is:
If
$$\left[\begin{array}{ll}
1 & 1 \\
0 & 1
\end{array}\right] \cdot\left[\begin{array}{ll}
1 & 2 \\
0 & 1
\end{array}\right] \cdot\left[\begin{array}{ll}
1 & 3 \\
0 & 1
\end{array}\right] \cdot \ldots \ldots \ldots . .\left[\begin{array}{cc}
1 & n-1 \\
0 & 1
\end{array}\right]=\left[\begin{array}{cc}
1 & 78 \\
0 & 1
\end{array}\right],
$$
then the inverse of $\displaystyle \left[\begin{array}{ll}1 & \mathrm{n} \\ 0 & 1\end{array}\right]$ is :
Official answer
(3)
$\displaystyle \left[\begin{array}{cc}
1 & -13 \\
0 & 1
\end{array}\right]$
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JEE Main 2019 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.