1. Choose the matrix in echelon form from the following:
{image} 1. 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. The system of linear equations {image} has a unique solution
The system of linear equations {image} has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination.
( 4, 5, 7 )
( 5, 7, 4 )
( 7, 4, 5 ) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. The system of linear equations {image} has a unique solution
The system of linear equations {image} has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination. Select the correct answer.
( 2, 1, 4 )
( 1, 4, 2 )
( 4, 2, 1 ) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. Determine whether the system of linear equations is inconsistent or dependent. If it is dependent, find the complete solution. {image}
{image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. 20 students in room A 50 students in room B 30 students in room C
A small school has 100 students who occupy three classrooms: A, B, and C. After the first period of the school day, half the students in room A move to room B, one - fifth of the students in room B move to room C, and one-third of the students in room C move to room A. Nevertheless, the total number of students in each room is the same for both periods. How many students occupy each room? Select the three correct answers.
20 students in room A
50 students in room B
30 students in room C
18 students in room A
27 students in room B
45 students in room C 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50