The matrix $N = \left[ {\begin{array}{*{20}{c}}{43}\{27}\end{array}} \right]\;\begin{array}{*{20}{c}}{Males}\{Females}\end{array}$ lists the number of males and females in a group of 70 people. The matrix P that lists the percentage of males and females in the same group of people is given by:

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BlackTom AI · Accepted Answer

The question presents a 2-by-1 column vector N = [43; 27], representing the counts of males and females in a group of 70 people. It then asks for the matrix P that lists the percentage of males and females in the same group.

Option analysis:
- Option c: P = [100/70] N
  This expression scales each count in N by 100/70, which converts counts to percentages since percentage is count divided by total times 100. Specifically, for the total of 70, multiplying by 100/70 yields the male percentage 43*(100/70) and the female percentage 27*(100/70). This aligns with the standard conversion from counts to percentages: percentage = (count / total) * 100. Therefore, applying the factor 100/70 to the vector N correctly yields the vector of percentages for males and females in the group.

Why other ideas (if considered) would be flawed:
- If one thought P should be simply N, that would give raw counts instead of percentages, which is not what is meant by a percentage matrix.
- If someone suggested a different scalar like 70/100, that would reverse the operation, producing values that do not represent percentages (they would sum to 1 after scaling, not to 100 per component).
- If there were a suggestion to apply a nonlinear transformation or to use a matrix that mixes the components (e.g., off-diagonal terms), that would be unnecessary and incorrect here because the male and female counts map directly to their respective percentages without interaction between components.

Overall, the essential reasoning is that converting counts to percentages in a fixed total group requires multiplying by 100/total, which in this case is 100/70. Hence, P = (100/70) N produces the desired percentage vector for males and females.

The matrix \(N = \left[ {\begin{array}{{20}{c}}{43}\\{27}\end{array}} \right]\;\begin{array}{{20}{c}}{Males}\\{Females}\end{array}\) lists the number of males and females in a group of 70 people. The matrix P that lists the percentage of males and females in the same group of people is given by:

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