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 428

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

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Definitions:

Demand Curve

The Demand Curve depicts the relationship between the price of a product and the amount of it that consumers are willing to purchase at various prices, usually sloping downward from left to right.

Dominant Firm

A company with a significant market share or influence, often capable of setting prices within its industry.

Price Leadership Model

A market condition where one leading company sets the price of goods or services, and other companies in the sector follow suit, either explicitly or implicitly.

Oligopolistic Industry

An industry characterized by a small number of large firms dominating the market, often leading to strategic interdependent pricing and production decisions.