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## Main Question or Discussion Point

Going through a mathematical physics book in the section about vector spaces, in the section showing how to prove vectors are linearly dependent their example is:

Two vectors in 3-d space:

are linearly dependent as we can write down

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I understand the concept of linear dependence, and why the answer makes sense (non-zero constants exist) but my question is how they determined the constants needed to show the vectors are dependent. My first thought was Gaussian elimination but I don't think that's correct.

Any help would be appreciated.

Two vectors in 3-d space:

**A**=**i**+ 2**j**-1.5**k****B**=**i**+**j**- 2**k****C**=**i**-**j**- 3**k**are linearly dependent as we can write down

2

**A**- 3**B**+**C**=**0**I understand the concept of linear dependence, and why the answer makes sense (non-zero constants exist) but my question is how they determined the constants needed to show the vectors are dependent. My first thought was Gaussian elimination but I don't think that's correct.

Any help would be appreciated.