Question

IS IT ALWAYS THE CASE THAT IF WE WANNA PROVE THAT A CERTAIN VECTOR IS LINEARLY INDEPENDENT WE EQUATE IT WITH ZERO VECTOR ?IF YES THEN WHY

Answer 1

no

Answer 2

Actually the opposite is TRUE :

Answer 3

Linearly independent means that If one wants to equate some combination of OldVectors & the Additional Vector to Zero vector - only the total "killing" of all of them with multipliing by zero each of them will do the trick

Answer 4

There is usally some simple independence EVIDENCE

Answer 5

Also, one vector not zero is always independent.

Answer 6

For Exmp. (7,3,0) and (0,23, 12) and ((0, 170, ) ARE linearly independent BECAUSE...

Answer 7

Intended to write (0, 170, 0)

Answer 8

IT is IMpossible to create zero in 2-nd coordinate using the first two given vectors without "UN-ZEROING" both 1-st and 3-rd coordinates

Answer 9

Soo the first two vectors CANNOT "kill" the third vector to form (0, 0 ,0)

Answer 10

Summarry: INDEPENDENT MEANS YOU CAN_NOT equate it to zero by others

Answer 11

BTW medal is expected...

Answer 12

@Mikael, the way u use "kill" makes linear algebra look like a bloody sport.