6. Exam and marks: Addition on 4×4 matrices

Two examinations were conducted for three groups of students, namely, group \(1\), group \(2\), and group \(3\) and their data on average of marks for the subjects Tamil, English, Science and Mathematics are shown below in the form of matrices \(A\) and \(B\). Determine the total marks of both the examinations for all three groups.

 

[Note: Columns of the matrix \(C_1, C_2, C_3, C_4\) refer the average marks of the subjects Tamil, English, Science and Mathematics, respectively. The rows of the matrix \(R_1, R_2, R_3\) refers the groups \(1, 2, 3\) respectively.]

 

\(A =\begin{bmatrix}
6 & 7 & 11 & 12\\ 
6 & 15 & 4 & 4\\ 
7 & 10 & 5 & 8
\end{bmatrix}, B = \begin{bmatrix}
3 & 11 & 8 & 3\\ 
10 & 2 & 15 & 8\\ 
11 & 5 & 6 & 7
\end{bmatrix}\)

 

The total marks of both the examinations for all the three groups is ________