Model Applied Situations with Matrix Operations
The $\perp$ Shape in the Figure Below Is Shown Using 9 Pixels

question 117

Multiple Choice

Model Applied Situations with Matrix Operations
The $\perp$ shape in the figure below is shown using 9 pixels in a $3 \times 3$ grid. The color levels are given to the right of the figure. Use the matrix $\left[ \begin{array} { l l l } 1 & 3 & 1 \\ 1 & 3 & 1 \\ 3 & 3 & 3 \end{array} \right]$ that represents a digital photograph of the $\perp$ shape to solve the problem.
-Using the same color levels from the instructions, write a 3 × 3 matrix A that represents the letter L in dark grey on a white background. Then find a 3 × 3 matrix B so that A + B lightens only the letter L from dark
Grey to light grey.

• A) \(A = \left[ \begin{array} { l l l } 2 & 0 & 0 \\ 2 & 0 & 0 \\ 2 & 2 & 2 \end{array} \right] ; B = \left[ \begin{array} { r r r } - 1 & 0 & 0 \\ - 1 & 0 & 0 \\ - 1 & - 1 & - 1 \end{array} \right]\)
• B) \(A = \left[ \begin{array} { l l l } 2 & 1 & 1 \\ 2 & 1 & 1 \\ 2 & 2 & 2 \end{array} \right] ; B = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \end{array} \right]\)
• C) \(A = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \end{array} \right] ; B = \left[ \begin{array} { r r r } - 1 & 0 & 0 \\ - 1 & 0 & 0 \\ - 1 & - 1 & - 1 \end{array} \right]\)
• D) \[A = \left[ \begin{array} { l l l } 3 & 1 & 1 \\ 3 & 1 & 1 \\ 3 & 3 & 3 \end{array} \right] ; B = \left[ \begin{array} { l l l } - 2 & - 1 & - 1 \\ - 2 & - 1 & - 1 \\ - 2 & - 2 & - 2 \end{array} \right]\]

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Definitions:

Good Faith Bargaining

The duty of both parties in a negotiation (e.g., employers and employees' union) to meet and negotiate at reasonable times with willingness to reach an agreement on matters under negotiation, such as wages, hours, and terms and conditions of employment.

Strike Capability

The ability of workers or a labor union to carry out a strike effectively in pursuit of their demands.

Interest Arbitration

A dispute resolution method where an impartial arbitrator makes binding decisions on labor-management disputes, especially during collective bargaining.

Plant Closings

The process of shutting down manufacturing facilities or plants, often leading to job losses and economic impacts on communities.