Help me with math

Linear Programming

Use the information below to answer questions 1 and 2.

You may also use the graph provided if it helps:

���, �� = 3� − � � ≤ 5 − � � ≤ − 1 0 ≤ � 0 ≤ �

1. Use linear programming methods to find the maximum

2. Use linear programming methods to find the minimum

Lagrange Multipliers

For questions 3-6, use the Lagrange Multiplier method for optimization to find the maximum of

the function : ���� = � − 4� subject to � + � = 9

____ 3. Write the Lagrange function, L x,y,λ( ).

____ 4. Find the system of equations to solve the optimization problem.

____ 5. Find all critical points.

____ 6. Find the maximum value of f (x,y).

Systems of Equations and Matrices

_______ 7. Write the following system as a matrix:

5� − 7� = 11� + 3� = 6

_______ 8. Perform operation R2 = 2r1 – r2 on the following:

��1 3 52 −4 14 7 2� −2−39 �

_______ 9. Given � = �1 32 −1�, � = �2 4 11 −2 3�, and � = �−1 5 −31 2 1 �

a) Can BA be calculated?

b) Can A – BC T be calculated?

_______ 10. Given � = � 1 4−2 3 , � = �2 −31 4 , and � = � 2 1−3 2 , solve CX = A

_______ 11. Recall the formula for the determinant of a matrix:

!"# � = ∑ &'(�−1�')( det-.'(/0(1'

Given � = 23 5 −21 −1 42 1 −33, the first term in the expansion of the determinant is &''�−1�')' det�.''� = �3��−1� det �−1 41 −3� = −3

Determine the second term.

Second term, j=2: &' �−1�') det�.' � = �5��−1�4det �1 42 −3� = 55

Scratch Work Below

Scratch Work Below