1.Formulate the situation as a system of linear equations. Be sure to state clearly the meaning of each variable. Solve using the Gauss-Jordan method. State your final answer in terms of the original question. (If the system is inconsistent, answer INCONSISTENT. If the system is dependent, parametrize the solutions in terms of the parametersuandv.)

A large commercial farm needs40,000pounds of potash,75,500pounds of nitrogen, and28,500pounds of phosphoric acid. Three brands of fertilizer, GrowRite, MiracleMix, and GreatGreen, are available and contain the amounts of potash, nitrogen, and phosphoric acid per truckload listed in the table. How many truckloads of each brand should be used to provide the required potash, nitrogen, and phosphoric acid?

x₁=truckloads of GrowRite

x₂=truckloads of MiracleMix

x₃=truckloads of GreatGreen

Pounds per

truckload)GrowRiteMiracleMixGreatGreen

Potash400600 700

Nitrogen50010001600

Phosphoric acid300400 500

2.Use the given matrix to find the expression.

A=916

954

758;A^t

A^t=

3.Use the given matrix to find the expression.

C=982

739

919;3C

3C=

4.Use the given matrix to find the expression.

B=493

841

965;B

B=

5.Use the given matrices to find the expression.

A=

251

854

736

C=

576

814

349;

A+C

A+C=

6.Use the given matrices to find the expression.

A=

293

154

636

C=

671

594

916;

C(A+I)

C(A+I)=