Answer to Question #203347 in Linear Algebra for Raghav sood

Question #203347

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.


1
Expert's answer
2021-06-14T10:41:17-0400

a)

132243312=5+35210=0\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:

66+48+92+214+61+24=1286\cdot6+4\cdot8+9\cdot2+2\cdot14+6\cdot1+2\cdot4=128



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