In Exercises 25–32, find the optimal value for the linear programming problem. Maximize the objective function x + 2 y subject to the constraints { y ≤ − x + 100 y ≥ 1 3 x 20 y ≤ x
In Exercises 25–32, find the optimal value for the linear programming problem. Maximize the objective function x + 2 y subject to the constraints { y ≤ − x + 100 y ≥ 1 3 x 20 y ≤ x
1 2
21. For the matrix A
=
3 4
find AT (the transpose of A).
22. Determine whether the vector
@
1
3
2
is perpendicular to
-6
3
2
23. If v1
=
(2)
3
and v2 =
compute V1 V2 (dot product).
.
7. Find the eigenvalues of the matrix
(69)
8. Determine whether the vector
(£)
23
is in the span of the vectors
-0-0
and
2
2
1. Solve for x:
2. Simplify:
2x+5=15.
(x+3)² − (x − 2)².
-
b
3. If a = 3 and 6 = 4, find (a + b)² − (a² + b²).
4. Solve for x in 3x² - 12 = 0.
-
Chapter 3 Solutions
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