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

question 49

Multiple Choice

Matrix A is given. Find appropriate identity matrices I_m and I_n such that I_mA = A and AI_n = A.
- $$A = \left[ \begin{array} { r r } 2 & - 7 \\6 & 0 \\- 6 & 9 \\7 & - 2\end{array} \right]$$

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

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Definitions:

Constraints

Restrictions or limitations on the variables of a problem which define the conditions or boundaries within which a solution must be found.

Experimental Statistical Study

A research method involving the manipulation of one variable to determine if changes in one variable cause changes in another variable.

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An infectious disease caused by the bacterium Vibrio cholerae, leading to severe diarrhea and dehydration.

Polio

A viral disease that can affect nerves and lead to partial or full paralysis, largely eradicated in many countries through vaccination.