Find the inverse of the matrix.
-$$\left[ \begin{array} { l l l }
1 & 0 & 0 \
5 & 1 & 0 \
0 & 7 & 1
\end{array} \right]$$
A) $\left[ \begin{array} { r r r } 1 & 0 & 0 \ - 5 & 1 & 0 \ 35 & - 7 & 1 \end{array} \right]$

B) $\left[ \begin{array} { r r r } 1 & 7 & - 35 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{array} \right]$

C) $\left[ \begin{array} { l l l } 1 & 0 & 0 \ 5 & 1 & 0 \ 0 & 0 & 7 \end{array} \right]$

D) $\left[ \begin{array} { r r r } 1 & 0 & 0 \ 7 & - 1 & 0 \ - 35 & 5 & 1 \end{array} \right]$

Question

Find the inverse of the matrix.
-$$\left[ \begin{array} { l l l } 
1 & 0 & 0 \
5 & 1 & 0 \
0 & 7 & 1
\end{array} \right]$$
A) $\left[ \begin{array} { r r r } 1 & 0 & 0 \ - 5 & 1 & 0 \ 35 & - 7 & 1 \end{array} \right]$

B) $\left[ \begin{array} { r r r } 1 & 7 & - 35 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{array} \right]$

C) $\left[ \begin{array} { l l l } 1 & 0 & 0 \ 5 & 1 & 0 \ 0 & 0 & 7 \end{array} \right]$

D) $\left[ \begin{array} { r r r } 1 & 0 & 0 \ 7 & - 1 & 0 \ - 35 & 5 & 1 \end{array} \right]$

Quizplus · Accepted Answer

The given matrix is a lower triangular matrix, and its inverse can be found by inverting each element on the diagonal (which are all 1, so they remain unchanged) and then changing the sign of the off-diagonal elements, taking into account their position relative to the diagonal. The correct inverse matrix is thus the one that correctly adjusts the off-diagonal elements according to these rules, which is option A.

Find the Inverse of the Matrix [100510071]\left[ \begin{array} { l l l } 1 & 0 & 0 \\5 & 1 & 0 \\0 & 7 & 1\end{array} \right]​150​017​001​​

Find the Inverse of the Matrix $\left[ \begin{array} { l l l } 1 & 0 & 0 \\5 & 1 & 0 \\0 & 7 & 1\end{array} \right]$