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Math 1050 Exam 3: Solving Systems of Equations and Finding Determinants - Prof. Derrick C., Exams of Mathematics

The november 29, 2006 math 1050 exam 3 for a college-level mathematics course. It includes various problems related to solving systems of linear equations using substitution, elimination, and matrix methods, as well as finding the determinant of a 2x2 matrix. Students are required to show all work for full credit.

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

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Math 1050 November 29, 2006 Exam 3 Name: 1
Exam 3
Prob. 1 2 3 4 5 6 7 EC
Value 13 12 10 15 15 15 20 5 100+5
Points
Show all work for credit. Answers with little or no supporting work will receive little or no credit. Your work should
be neat; if I cannot read your work, it will not be graded.
1. Find all solutions to the set of equations:
2xy= 1
x+3y= 4
2. Find all values of a,b,c, and dso that
a9
6d=4b
c19
3. Write the following system of linear equations in the form of a matrix.
3x5y+4z= 10
4x+2y3z=12
x+z=2
pf3
pf4

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Math 1050 November 29, 2006 Exam 3 Name: 1

Exam 3 Prob. 1 2 3 4 5 6 7 EC Value 13 12 10 15 15 15 20 5 100+ Points

Show all work for credit. Answers with little or no supporting work will receive little or no credit. Your work should be neat; if I cannot read your work, it will not be graded.

  1. Find all solutions to the set of equations:

2 x −y = 1 x +3y = 4

  1. Find all values of a, b, c, and d so that (^) [ a 9 6 d

]

[

4 b c 19

]

  1. Write the following system of linear equations in the form of a matrix.

3 x − 5 y +4z = 10 4 x +2y − 3 z = − 12 −x +z = − 2

  1. Fill in the missing entries by preforming the indicated row operations.  

 R^2 −→−^3 R^1

  1. Find all values of x, y, and z so that  

3 2 z 1 7 − 5 1 y 1

1 x − 3 2

  1. The Determinate of a 2 × 2 matrix is defined as

a b c d =^ ad^ −^ bc.

(a) Find

(b) Find an a so that

a 5

Bonus: The determinate for a 3 × 3 matrix is defined as

a b c d e f g h i

= a · e f h i − d · b c h i

  • g · b c e f

Evaluate 1 2 3 4 5 6 7 8 9