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:

Isomorphism

A concept in sociology that refers to the process by which organizations in the same sector or context become increasingly similar to each other in structure and function.

Hybrid System

A combination of different technologies, methodologies, or systems that integrate to function together, often bringing together the best features of each.

Closed

This term could refer to an entity, system, or status that is not open for operation, participation, or access by the public or specific groups.

Open

Available to all, not restricted or exclusive, often used in the context of data or software that can be freely accessed and modified.