Model Applied Situations with Matrix Operations
-Using the Same Color

question 47

Multiple Choice

Model Applied Situations with Matrix Operations
-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)
• \(A = \left[ \begin{array} { l l l } 2 & 0 & 0 \\ 2 & 0 & 0 \\ 2 & 2 & 2 \end{array} \right] ; B = \left[ \begin{array} { r r r } - 1 & 0 & 0 \\ - 1 & 0 & 0 \\ - 1 & - 1 & - 1 \end{array} \right]\)
• \(\mathrm { A } = \left[ \begin{array} { l l l } 2 & 1 & 1 \\ 2 & 1 & 1 \\ 2 & 2 & 2 \end{array} \right] ; \mathrm { B } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \end{array} \right]\)
• B)
• \(\mathrm{A}=\left[\begin{array}{lll}
• 2 & 1 & 1 \\
• 2 & 1 & 1 \\
• 2 & 2 & 2
• \end{array}\right] ; \mathrm{B}=\left[\begin{array}{lll}
• 1 & 0 & 0 \\
• 1 & 0 & 0 \\
• 1 & 1 & 1
• \end{array}\right]\)
• 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:

CTU Instruction

A command used in PLC (Programmable Logic Controller) programming to count upwards towards a preset value, often used in automation for tracking or controlling processes.

Counter Structure

A programming construct used to store the number of occurrences or iterations, often used in loops or to track events.

Retains Accum

A function or method in PLCs or similar systems that allows the accumulation of data or values to be retained even after power loss or system restart.

Rung Goes False

In ladder logic programming for PLCs, this refers to the condition where the conditions for a particular rung are not met, leading to a false or "off" state.