Find the Matrix Product When Possible $A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & 1 & 1 \\ - 1 & 0 & - 1 \end{array} \right]$

question 134

Multiple Choice

Find the matrix product when possible.
-Given $A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & 1 & 1 \\ - 1 & 0 & - 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 1 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 1 & 0 \end{array} \right]$ , find $A B$ and $B A$ .

• A)
• \(\mathrm { AB } = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & - 1 & 0 \\ - 1 & 0 & 0 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & - 1 & 0 \\ - 1 & 0 & 0 \end{array} \right]\)
• B)
• \(\mathrm { AB } = \left[ \begin{array} { c c c } 0 & 2 & 1 \\ 0 & - 1 & - 1 \\ 0 & 0 & 1 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { c c c } 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & - 2 & 0 \end{array} \right]\)
• C)
• \(A B = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 1 & 2 & 0 \\ 0 & - 2 & 0 \end{array} \right] ; B A = \left[ \begin{array} { c c c } 0 & 0 & - 1 \\ 0 & 1 & 1 \\ 0 & - 2 & - 1 \end{array} \right]\)
• D)
• \(\mathrm { AB } = \left[ \begin{array} { r r r } 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & - 2 & 0 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { c c c } 0 & 2 & 1 \\ 0 & - 1 & - 1 \\ 0 & 0 & 1 \end{array} \right]\)

Learn how to estimate population sizes using different methods, including the mark-recapture technique.

Understand factors affecting population size, including birth, death, immigration, and emigration.

Learn about population density and its impact on growth rates and behaviors.

Understand the implications of density-dependent and density-independent regulatory factors on population dynamics.

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