Let no. of students in Ist, 2nd and 3rd group to x, y, z respectively.

From the statement we have

x + y+ z = 10

2x + y =13

x + y – 4z = 0

The above system of linear equations may be written in matrix form as AX = B where

Now, A_{11} = – 4 – 0 = –4

A_{12} = – (–8 – 0) = 8

A_{13} = 2 – 1 = 1

A_{21} = –(–4 – 1) = 5

A_{22 }= –4 – 1 = –5

A_{23} = –(1 – 1) = 0

A_{31} = 0 – 1 = –1

A_{32} = –(0 – 2) = 2

A_{33 }= 1 – 2 = –1