Answer to Question #203347 in Linear Algebra for Raghav sood

Question

a) Is the set of vectors {(1,2,3), (3,4,1),(2,3,2)} linearly independent? Give reasons for the answer.

6 4 1 5 14

8 9 2 7 16

4 3 6 2 5

6 10 15 4

b) Find an initial basic feasible solution to the following transportation problem by the North-West corner method. Verify whether your solution is optimal.

Answer 1

a)

$\begin{vmatrix} 1 & 3 &2\\ 2 & 4&3\\ 3&1&2 \end{vmatrix}=5+3\cdot5-2\cdot10=0$

The vectors are linearly dependent.

b)

Optimal solution:

$6\cdot6+4\cdot8+9\cdot2+2\cdot14+6\cdot1+2\cdot4=128$