Maths Midterm Review Exam

1. Solve the system of linear equations, using the Gauss-Jordan elimination method.

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2.  Consider the linear programming problem.

Sketch the feasible set for the linear programming problem.

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3. Indicate whether the matrix is in row-reduced form.

[removed]A) The matrix is in row-reduced form.
[removed]B) The matrix is not in row-reduced form.

4.  Write the equation   in the slope-intercept form and then find the slope and y-intercept of the corresponding line.

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5. Solve the linear system of equations

[removed]A) Unique solution: 

[removed]B) Unique solution: 

[removed]C) Infinitely many solutions: 

[removed]D) No solution

6. Solve the linear system of equations

[removed]A) Unique solution: 

[removed]B) Unique solution: 

[removed]C) Infinitely many solutions: 

[removed]D) No solution

7.  Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. 8x = 5y + 9

[removed]A) y =  x +   

[removed]B) y = x -

[removed]C) y =  -x -

[removed]D) y = -x +

[removed]E) y is not a linear function of x.

8. Check that the given simplex tableau is in final form. Find the solution to the associated regular linear programming problem.

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9.  Metro Department Store's annual sales (in millions of dollars) during 5 years were

Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.

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10. If the line passing through the points (2, a) and (5, - 3) is parallel to the line passing through the points (4, 8) and (- 5, a + 1) , what is the value of a?

[removed]A) a = -8
[removed]B) a = 4
[removed]C) a = -4
[removed]D) a = 8

11. Maximize

P= 10x + 12y

subject to

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12. Solve the linear programming problem by the simplex method.

[removed]A) x = 16, y = 0, z = 16, t = 0, u = 80, v = 21, w = 61, P = 180
[removed]B) x = 0, y = 16, z = 0, t = 0, u = 80, v = 21, w = 61, P = 96
[removed]C) x = 80, y = 16, z = 0, t = 0, u = 0, v = 21, w = 61, P = 68
[removed]D) x = 80, y = 0, z = 0, t = 16, u = 80, v = 21, w = 61, P = 174

13. Find the slope of the line that passes through the given pair of points.

(2, 2) and (8, 5)

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[removed]B) 2
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14. Check that the given simplex tableau is in final form. Find the solution to the associated regular linear programming problem.

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15. Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.

[removed]A) one and only one solution 

[removed]B) one and only one solution 

[removed]C) one and only one solution 

[removed]D) infinitely many solutions 

[removed]E) no solution

16. Find the pivot element to be used in the next iteration of the simplex method.

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17. Find an equation of the line that passes through the points (1, 4) and ( -7, -4)

[removed]A) y = 7x + 7
[removed]B) y = x + 3
[removed]C) y = 3x - 7
[removed]D) y = 3x – 3

18. Find the constants m and b in the linear function f(x) = mx + b so that f(1) = 2 and the straight line represented by f has slope - 1.

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19. Solve the linear system of equations

[removed]A) Unique solution: 

[removed]B) Unique solution:

[removed]C) Infinitely many solutions:

[removed]D) No solution

20. Determine whether the given simplex table is in the final form. If so, find the solution to the associated regular linear programming problem.

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21. Solve the system of linear equations using the Gauss-Jordan elimination method.

[removed]A) ( 7, –3 )
[removed]B) ( 6, –2 )
[removed]C) ( 2, –6 )
[removed]D) ( –6, 2 )
[removed]E) ( –7, –2 )

22. Consider the linear programming problem.

Sketch the feasible set for the linear programming problem.

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23. Solve the system of linear equations using the Gauss-Jordan elimination method.

[removed]A) ( 0, 2 )
[removed]B) ( 8, 2 )
[removed]C) ( 4, –6 )
[removed]D) ( –2, 4 )
[removed]E) ( 4, –2 )

24. Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b.

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[removed]E) y is not a linear function of x.

 25. Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.

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