Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary.
-$$\left[ \begin{array} { r r r r }
1 & - 9 & 0 & 0 \
0 & 1 & - 7 & 0 \
0 & 0 & 1 & 1 \
0 & 0 & 0 & 1
\end{array} \right]$$
A) $\left[ \begin{array} { r r r r } 1 & 0 & 0 & 0 \ - 1 & 1 & 0 & 0 \ 7 & 7 & 1 & 0 \ - 63 & - 63 & 9 & 1 \end{array} \right]$

B) $\left[ \begin{array} { r r r r } 1 & 0 & 0 & 0 \ 9 & 1 & 0 & 0 \ 63 & 7 & 1 & 0 \ - 9 & - 7 & - 1 & 1 \end{array} \right]$

C) $\left[ \begin{array} { c c c c } 1 & 9 & 63 & - 63 \ 0 & 1 & 7 & - 7 \ 0 & 0 & 1 & - 1 \ 0 & 0 & 0 & 1 \end{array} \right]$

D) $\left[ \begin{array} { r r r r } 1 & - 1 & 7 & - 63 \ 0 & 1 & 7 & - 63 \ 0 & 0 & 1 & 9 \ 0 & 0 & 0 & 1 \end{array} \right]$

Question

Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary.
-$$\left[ \begin{array} { r r r r } 
1 & - 9 & 0 & 0 \
0 & 1 & - 7 & 0 \
0 & 0 & 1 & 1 \
0 & 0 & 0 & 1
\end{array} \right]$$
A) $\left[ \begin{array} { r r r r } 1 & 0 & 0 & 0 \ - 1 & 1 & 0 & 0 \ 7 & 7 & 1 & 0 \ - 63 & - 63 & 9 & 1 \end{array} \right]$

B) $\left[ \begin{array} { r r r r } 1 & 0 & 0 & 0 \ 9 & 1 & 0 & 0 \ 63 & 7 & 1 & 0 \ - 9 & - 7 & - 1 & 1 \end{array} \right]$

C) $\left[ \begin{array} { c c c c } 1 & 9 & 63 & - 63 \ 0 & 1 & 7 & - 7 \ 0 & 0 & 1 & - 1 \ 0 & 0 & 0 & 1 \end{array} \right]$

D) $\left[ \begin{array} { r r r r } 1 & - 1 & 7 & - 63 \ 0 & 1 & 7 & - 63 \ 0 & 0 & 1 & 9 \ 0 & 0 & 0 & 1 \end{array} \right]$

Quizplus · Accepted Answer

The given matrix is an upper triangular matrix with all diagonal elements as 1, making it invertible. The inverse of an upper triangular matrix with ones on the diagonal is also upper triangular with specific elements calculated to satisfy the identity matrix condition. Option C correctly represents this inverse.

Use a Graphing Utility to Find the Inverse of the Matrix