Matrix A is given. Find appropriate identity matrices I m and I n such that I m A = A and AI n = A.
-$$A = \left[ \begin{array} { r r }
2 & - 7 \
6 & 0 \
- 6 & 9 \
7 & - 2
\end{array} \right]$$
A) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right]$
B) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right]$
C) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{array} \right]$
D) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right]$

Question

Matrix A is given. Find appropriate identity matrices I m and I n such that I m A = A and AI n = A.
-$$A = \left[ \begin{array} { r r } 
2 & - 7 \
6 & 0 \
- 6 & 9 \
7 & - 2
\end{array} \right]$$
A) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right]$
B) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right]$
C) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{array} \right]$
D) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right]$

Quizplus · Accepted Answer

Matrix A is a 4x2 matrix. The identity matrix $\mathrm { I } _ { \mathrm { m } }$ that satisfies $\mathrm { I } _ { \mathrm { m } }A = A$ must be a 4x4 matrix, and the identity matrix $\mathrm { I } _ { \mathrm { n } }$ that satisfies $A\mathrm { I } _ { \mathrm { n } } = A$ must be a 2x2 matrix.

Matrix a Is Given A=[2−760−697−2]A = \left[ \begin{array} { r r } 2 & - 7 \\6 & 0 \\- 6 & 9 \\7 & - 2\end{array} \right]A=​26−67​−709−2​​

Matrix a Is Given $A = \left[ \begin{array} { r r } 2 & - 7 \\6 & 0 \\- 6 & 9 \\7 & - 2\end{array} \right]$