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

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

C) $\left[ \begin{array} { r r r } 1 & 0 & 0 \ 1 & 1 & 0 \ - 2 & - 1 & 1 \end{array} \right]$

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

Question

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

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

C) $\left[ \begin{array} { r r r } 1 & 0 & 0 \ 1 & 1 & 0 \ - 2 & - 1 & 1 \end{array} \right]$

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

Quizplus · Accepted Answer

The inverse of a lower triangular matrix can be found by reversing the signs of the off-diagonal elements. The given matrix is lower triangular, and option C is the correct inverse.

Find the Inverse of the Matrix [100−110111]\left[ \begin{array} { r r r } 1 & 0 & 0 \\- 1 & 1 & 0 \\1 & 1 & 1\end{array} \right]​1−11​011​001​​

Find the Inverse of the Matrix $\left[ \begin{array} { r r r } 1 & 0 & 0 \\- 1 & 1 & 0 \\1 & 1 & 1\end{array} \right]$