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The solutions to test 3 of math 140 (spring 2005) covering topics such as systems of equations, inequalities, and matrices. Students will find answers to questions involving finding the solution to systems of equations, graphing the solution set of inequalities, maximizing an objective function, and performing matrix arithmetic.
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Math 140. Test 3 (Spring 2005. Harvey).
Name (5 points):
No notes or texts allowed. You may use a TI-83, TI-84, TI-86 or equivalent calculator. Show all work.
1 (6 points). Find the solution to this system of equations: { x − y = 3 2 x − 3 y = − 3
2 (10 points). Find the solution to this system of equations:
x + y + 2z = 9 2 x + y + z = 10 x + 3z = 7
3 (8 points). You are offered two jobs as a salesperson. One company offers an annual salary of $25, 000 plus a year end bonus of 2% of your total sales. The other company offers an annual salary of $20, 000 plus a year end bonus of 3% of your total sales. Determine the annual sales required to make the second offer better.
4 (10 points). Graph the solution set of the system of inequalities:
x ≥ 0 x + y ≥ 0 x^2 + y ≤ 2
Label all corner (intersection) points.
7 (6 points). Perform the indicated matrix arithmetic:
( 2 3 3 1
8 (6 points). Solve for x, y, z, and w:
( x 2 4 1
y 12 z w
9 (8 points).
A =
Calculate both A × B and B × A (if possible).
10 (10 points).
A =
Compute A−^1. Show your work (no calculator).
