Mathematics

Mathematics

Problem

The marks (out of 100) obtained by three students in four unit tests are recorded below. The first matrix shows marks in Mathematics and the second shows marks in Physics. M=[788592886475708090939591],P=[827988846972787687919089]M=\begin{bmatrix}78&85&92&88\\64&75&70&80\\90&93&95&91\end{bmatrix}, \quad P=\begin{bmatrix}82&79&88&84\\69&72&78&76\\87&91&90&89\end{bmatrix} Rows correspond to students S1, S2, S3S_1,\,S_2,\,S_3 and columns correspond to Tests T1T_1 to T4T_4. (i) Form a new matrix DD that represents, for every student and every test, the difference (Mathematics mark)−(Physics mark)(\text{Mathematics mark})-(\text{Physics mark}). (ii) Identify for which test each student scored higher in Physics than in Mathematics by inspecting matrix DD. (iii) Calculate the total difference in marks (Mathematics minus Physics) for each student across all four tests.
Intuitive explanation

Matrix subtraction is the natural tool for comparing paired numerical data—here, two sets of scores for the same students and tests. Once you subtract PP from MM element-wise, the resulting matrix DD tells you instantly which subject each student performed better in (positive means Math ahead, negative means Physics ahead). Summing each row of DD then gives you each student's overall strength gap between the two subjects.

Intuitive explanation

Matrix subtraction is the natural tool for comparing paired numerical data—here, two sets of scores for the same students and tests. Once you subtract PP from MM element-wise, the resulting matrix DD tells you instantly which subject each student performed better in (positive means Math ahead, negative means Physics ahead). Summing each row of DD then gives you each student's overall strength gap between the two subjects.

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