Assume det  where  Find the determinant of the matrix 

Which of the following sets are subspaces of ? (1) 

Let  and  be 

Let  be a 

Use Cramer’s rule to complete the solution to  for the following system of equations: 

Which of the following defines a linear transformation from  to ? 

Consider the matrices 

Let , and . What is the geometric description of the Span ? 

CoolAir Corporation manufactures portable window air conditioners. CoolAir has the capacity to manufacture and sell 80,000 air conditioners each year but is currently only manufacturing and selling 60,000. The following per unit numbers relate to annual operations at 60,000 units:     Per Unit   Selling price $ 125 Manufacturing costs:     Variable $ 25 Fixed $ 40 Selling and administrative costs:     Variable $ 10 Fixed $ 15   The City of Clearwater would like to purchase 3,000 air conditioners from CoolAir but only if they can get them for $75 each. Variable selling and administrative costs on this special order will drop down to $2 per unit. This special order will not affect the 60,000 regular sales and it will not affect the total fixed costs. What is the annual financial advantage (disadvantage) for the company as a result of accepting this special order from the City of Clearwater?

The Michael Scott Paper Company uses customers served as its measure of activity. During February, the company budgeted for 35,000 customers, but actually served 34,000 customers. The company uses the following revenue and cost formulas in its budgeting, where q is the number of customers served: Revenue: $3.50q Wages and salaries: $33,200 + $1.10q Supplies: $0.50q Insurance: $10,400 Miscellaneous expense: $6,400 + $0.30q   The company reported the following actual results for February: Revenue $119,800 Wages and salaries $68,000 Supplies $14,400 Insurance $10,400 Miscellaneous expense $17,700 Prepare the company’s flexible budget performance report for February. Label each variance as favorable (F) or unfavorable (U)