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Math 140-02, Exam IIIA Name _________________________
There are 9 problems on this exam. Carefully read and follow all directions. In order to
receive credit show all necessary work. No credit will be given for an answer I cannot find
or cannot read.
- Let B =
(a) By hand, calculate the determinant of B. (3 points)
(b) Determine B
- 1 . Write your answer as a scalar times a matrix with integer entries. (5 points)
- Let C =
(a) Use your calculator to calculate the determinant of C. (3 points)
(b) Determine C
- 1 . Write your answer as a scalar times a matrix with integer entries. (5 points)
- Consider the following system of equations.
4x – 4y – z = 3
2x – 2y – 3z = – 4
(a) What is the coefficient matrix associated with this system? Label your answer as A. (3 points)
(b) Use your calculator to calculate the determinant of A. (3 points)
(c) Determine A-1. Write your answer as a scalar times a matrix with integer entries. (5 points)
(d) Write this system of equations as a matrix equation. (4 points)
(e) What matrix product must be calculated to find the solution of this system? (4 pts)
(f) Calculate the matrix product in part e and determine the solution of this system. (5 points)
x
y
- Use the graph of the function F shown below to determine the following. (3 points each)
(a) Domain of F (b) Range of F
(c) F(3)
- Use the function G(x) = 2 – 3x 2 to determine the following. (3 points each)
(a) Domain of G (b) Range of G
(c) G(2) (d) G(0)
(e) Simplify G(a + 2).
- Use Cramer’s rule (determinants) to solve the following system of equations. Show all
determinants that must be calculated. (8 points)
2x + 3y = 7
2x + 4y = 5
- Consider the system 4x + 2y + 5z = 8
2x – 3y + z = 13
y + 2z = 1
(a) List the two matrices whose determinants would have to be calculated in order to find the value of “z” in the solution of this system. (4 points)
(b) Use your calculator to calculate the determinants in part a and determine the value of “z” in the solution of this system. (4 points)
(c) Use the substitution method to find the values of “x” and “y” in the solution of this system. (4 points)
