Find the inverse of the invertible matrix.
-$\left[ \begin{array} { l l l } 1 & 0 & 0 \ 4 & 1 & 0 \ 0 & 3 & 1 \end{array} \right]$
A) $\left[ \begin{array} { r r r } 1 & 3 & - 12 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{array} \right]$
B) $\left[ \begin{array} { r r r } 1 & 0 & 0 \ - 4 & 1 & 0 \ 12 & - 3 & 1 \end{array} \right]$
C) $\left[ \begin{array} { l l l } 1 & 0 & 0 \ 4 & 1 & 0 \ 0 & 0 & 3 \end{array} \right]$
D) $\left[ \begin{array} { r r r } 1 & 0 & 0 \ 3 & - 1 & 0 \ - 12 & 4 & 1 \end{array} \right]$

Question

Quizplus · Accepted Answer

The inverse of a lower triangular matrix is also a lower triangular matrix, and the inverse can be found by inverting each diagonal element and negating the off-diagonal elements, adjusting them according to the multiplicative relationships in the original matrix. The correct inverse matrix is option B, which correctly inverts and adjusts the elements according to these rules.

Find the Inverse of the Invertible Matrix [100410031]\left[ \begin{array} { l l l } 1 & 0 & 0 \\ 4 & 1 & 0 \\ 0 & 3 & 1 \end{array} \right]​140​013​001​​

Find the Inverse of the Invertible Matrix $\left[ \begin{array} { l l l } 1 & 0 & 0 \\ 4 & 1 & 0 \\ 0 & 3 & 1 \end{array} \right]$