6. Solve the following system for x, y, and z:
 

7. Solve the following system for x, y, and z in terms of a, b, and c:
 

8. Show the following for the determinant

(a) D = a₁M₁ - a₂M₂ + a₃M₃, where M₁, M₂, and M₃ are the minors of a₁, a₂, and a₃ respectively.

(b) D = a₂A₂ + b₂B₂ + c₂C₂, where A₂, B₂, and C₂ are the cofactors of a₂, b₂, and c₂, respectively.

9. Show the following for the determinant

(a) a₃₁M₂₁ - a₃₂M₂₂ + a₃₃M₂₃ = 0.

(b) a₁₁C₁₃ + a₂₁C₂₃ + a₃₁C₃₃ = 0.
 

Wednesday, June 10, 1998