Find the Products AB and BA to Determine Whether B

question 21

Multiple Choice

Find the products AB and BA to determine whether B is the multiplicative inverse of A.
- $$A = \left[ \begin{array} { r r r r } 2 & 0 & 1 & 1 \\1 & 1 & - 1 & - 1 \\- 1 & - 2 & 1 & 0 \\0 & 0 & 1 & 1\end{array} \right] , \quad B = \left[ \begin{array} { r r r r } 2 & 0 & 0 & - 2 \\- 2 & 1 & 0 & 3 \\- 2 & 2 & 1 & 5 \\2 & - 2 & - 1 & - 3\end{array} \right]$$

• A) \(B \neq A ^ { - 1 }\)
• B) \(\mathrm { B } = \mathrm { A } ^ { - 1 }\) Find the inverse of the matrix, if possible.

Understand the geographical distribution of various biomes globally.

Recognize the characteristic flora and fauna associated with different biomes.

Comprehend the ecological importance of biodiversity within each biome.

Analyze the adaptation strategies of plants and animals in distinct biomes.

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Definitions:

Warning Coloration

Bright and distinctive patterns or colors on animals that serve to warn predators of their toxicity or unpalatability.

Ecological Niche

The role and position a species has in its environment; how it meets its needs for food and shelter, how it survives, and how it reproduces.

Density-dependent Factor

A factor whose effects on the size or growth of a population vary with the population density.

Bubonic Plague

An infectious disease caused by the bacterium Yersinia pestis, characterized by swollen lymph nodes, fever, and skin lesions.