Reduced the matrix with gauss-jordan elimination

Question

Which of the following is the solution to system

3x + 4y = 7
x + 2y = 2

Answer

• (x = 6, y = -2)
• (x = 5, y = -2)
• (x = 4, y = -1/2)
• (x = 3, y = -1/2)

Question 2

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution.
2x - 3y = 2
6x - 9y = 8

Answer

• one solution
• infinitely many solutions
• no solution
• can not tell

Question 3

Solve the linear system of equations x +4y =9, 0.5x + 2y = 4.5.

Answer

• Unique solution: (1, 2)
• Unique solution (4, 1 )
• Infinitely many solutions; (9-4k, k)
• No solution.

Question 4

A farmer has 400 acres available for cultivating crops A and B. He has a maximum of 13,200 hours of labor available. The labor required for cultivation crop A is 20 hours per acre and for crop B is 30 hours per acre.
Write the system of equations needed to determine how many acres of each crop should the farmer plant if he wishes to utilize all his resources.

(Let x = number of acres for cultivating crop A, y = number of acres for cultivating crop B).

Answer

• x+y = 400
  20x+30y=13200
• x+30y= 400
  x+20y =13200
• x+y= 400
  20x+4z=11200
• none of the above

Question 5

A restaurant manager wants to purchase 200 sets of dishes. One design costs $25 per set, while another costs $45 per set. If she only has $7400 to spend, how many of each design should be ordered?

Answer

• 110 $25 sets and 90 $45 sets
• 100 $25 sets and 100 $45 sets
• 120 $25 sets and 80 $45 sets
• 80 $25 sets and 120 $45 sets

Question 6

Determine the value of k for which the system of linear equations has no solution.

2x -y = 3,
4x + ky = 5

Answer

• -2
• 5/3
• 2
• -4

Question 7

Write the augmented matrix corresponding to the given system of equations.

2x - 3y =4
3x - 2y =5

Answer

• [2 -3]
  [3 -2]
• [2 3]
  [-3 -2]
• [2 -3 4]
  [3 -2 5]
• [4 2 -3]
  [5 3 -2]

Question 8

Which of the followings is not in row reduced form?

Answer

• [1 0| 2]
  [0 0| 3]
• [1 0| 2]
  [0 1| 3]
• [1 2 0| 1]
  [0 0 1| 3]
  [0 0 0| 0]
• [1 1 0| 0]
  [0 1 0| 0]
  [0 0 0| 0]

Question 9

Given matrix

[1 2 3| -1]
[2 1 -1| 2]
[-1 0 5| 7]

What will be the new second row after the row operation: R2-2R1+R3?

Answer

• [0, -3, -7 |4]
• [-1, -3, -2 | 11]
• [1, 1, 4 | 9]
• [0, 0, 1 | 2]

Question 10

With Gauss-Jordan elimination, the following matrix can be reduced to the reduced form

[1 2| 3]
[2 3| 4]

Answer

• [1 2 | 3]
  [0 -1 | -2]
• [1 0 | -1]
  [0 1 | 2]
• [1 0 | -1]
  [1 1 | 1]
• [1 1 | 1]
  [0 1 | 2]