14. Evaluate 

15. Show that in a three by three determinant if the elements of one row are a constant k times the elements of another row, then the determinant equals zero.
 

16. (a) Use the definition of a determinant to show that

(b) Show that if the elements of a given row of a three by three determinant D are f₁ + g₁, f₂ + g₂, f₃ + g₃, then D = D₁ + D₂ where D₁ results from D by replacing the given row by f₁, f₂, f₃ and D₂ by replacing the given row by g₁, g₂, g₃.
 

17. Show that if two rows of a three by three determinant D are u₁, u₂, u₃ and v₁, v₂, v₃, respectively, and if D^* is the same as the determinant D except that the row u₁, u₂, u₃ is replaced by u₁ + kv₁, u₂ + kv₂, u₃ + kv₃ where k is a constant, then D^* = D.
 

Wednesday, June 10, 1998