I was doing some problems on linear dependance and spanning that had parameters and i wasn't sure how to tell if i got the full answers. Here're two of them:(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Q1: Find all values of m so that the vectors:

{(1-m,2,7),(0,-2-m,12),(0,0,-m)} are linearly dependant.

Q2: Find all values of k so that the vectors:

{(1,2,k),(0,1,k-1),(3,4,3)} span R^3.

2. Relevant equations

Q1: vectors are linearly dependent if and only if one of the vectors is a linear combination of the others

Q2: 3 vectors span R^3 if and only if they're linearly independent.

3. The attempt at a solution

For Q1 i got: m=0,-2,1

For Q2 i got: k != 1 - in other words, everything except 1.

Are those answers right? How can i make sure that those are the only ones?

Thanks.

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# Linear Algebra - parameters

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