06 Jul Algebra Assignment
Please solve the following problems AND EXPLAIN STEP BY STEP HOW EACH PROBLEM WAS CALCULATED. I NEED TO UNDERSTAND HOW THESE ARE SOLVED:
1. 6.1 Exercise Set, Problem #40
Solve using the elimination method. Also determine whether each system is consistent or inconsistent and whether the equations are dependent or independent.
2. 6.2 Exercise Set, Problem #30
Investment. Walter earns a year-end bonus of $5000 and puts it in 3 one-year investments that pay $243 in simple interest. Part is invested at 3%, part at 4%, and part at 6%. There is $1500 more invested at 6% than at 3%. Find the amount invested at each rate.
3. 6.3 Exercise Set, Problem #18
Solve the system of equations using Gaussian elimination or Gauss-Jordan elimination.
4. 6.4 Exercise Set, Problem #36
Profit. A manufacturer produces exterior plywood, interior plywood, and fiberboard, which are shipped to two distributors. The following table shows the number of units of each type of product that are shipped to each warehouse.
| Distributor 1 | Distributor 2 | |
| Exterior Plywood | 900 | 500 |
| Interior Plywood | 450 | 1000 |
| Fiberboard | 600 | 700 |
The profits from each unit of exterior plywood, interior plywood, and fiberboard are $8, $10, and $7, respectively.
· a) Write the information in the table as a 3 × 2 matrix M.
· b) Write a row matrix P that represents the profit per unit of each type of product.
· c) Find the product PM.
· d) State what the entries of PM represent.
5. 6.5 Exercise Set: Problem #32
Solve the system of equations using the inverse of the coefficient matrix of the equivalent matrix equation.
6. 6.6 Exercise Set: Problem #38
Solve using Cramer’s rule.
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