Matrix a Is Given $$A = \left[ \begin{array} { r r r } 3 & 0 & - 8 \\1 & 8 & - 8 \\- 1 & - 1 & - 2\end{array} \right]$$

question 41

Multiple Choice

Matrix A is given. Find appropriate identity matrices I_m and I_n such that I_mA = A and AI_n = A.
- $$A = \left[ \begin{array} { r r r } 3 & 0 & - 8 \\1 & 8 & - 8 \\- 1 & - 1 & - 2\end{array} \right]$$

• A) \(\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right]\)
• B) \(\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]\)
• C) \(\mathrm { I } _ { \mathrm { m } } = \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]\)
• D) \(\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]\)

---

Definitions:

Private Partnerships

A business organization owned by two or more individuals who share management and profits or losses.

Arbitrage Profit

Earnings generated by exploiting the price differences of identical or similar financial instruments on different markets or in different forms.

Oil Futures

Oil futures are contracts to buy or sell oil at a predetermined price on a specified future date, used for hedging or speculation on oil price movements.

Risk-Free Rate

The rate of return on an investment with no risk of financial loss, typically associated with government bonds.