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 ________