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Consider four vectors v1 = [1,1,1,1], v2 = [-1,0,1,2], v3 = [a,1,0,b], and v4 = [3,2,a+b,0],...

Consider four vectors v1 = [1,1,1,1], v2 = [-1,0,1,2], v3 = [a,1,0,b], and v4 = [3,2,a+b,0], where a and b are parameters. Find all conditions on the values of a and b (if any) for which:

1. The number of linearly independent vectors in this collection is 1.

2. The number of linearly independent vectors in this collection is 2.

3. The number of linearly independent vectors in this collection is 3.

4. The number of linearly independent vectors in this collection is 4.

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